DSWiki - Вклад [ru]

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2024-09-20T09:19:13Z

Ivan Shilin:

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==



* [https://www.hse.ru/our/news/876470885.html Интервью Юлия Сергеевича "Вышке для своих" (30 ноября 2023)]
* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==

* [http://www.dyn-sys.org/w/images/d/df/Ilyashenko_2024_stability.pdf "Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields"] by Yu. Ilyashenko, Journal of Fixed Point Theory and Applications, V. 26, article 24, 2024.
* [http://www.dyn-sys.org/w/images/8/8c/Ilyashenko_2024_SN_Dulac_maps.pdf "Dulac maps of real saddle-nodes"] by Yu. Ilyashenko, Nonlinearity, V. 37, No. 10, 2024.
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

* Статья Диего М. Бенардета:

[https://www.tandfonline.com/doi/pdf/10.1080/00029890.2022.2005389 "Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model" by Diego M. Benardete (the paper expounds Yu. S. Ilyashenko's method of obtaining an upper bound on the number of limit cycles and applies this methos to a neural model)]

* Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса:
[http://www.dyn-sys.org/w/images/a/af/Ilyashenko_-_SelMathSov.pdf "Weakly Contracting Systems and Attractors of Galerkin Approximations of Navier-Stokes Equations on the Two-Dimensional Torus", 1992]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Файл:Ilyashenko 2024 SN Dulac maps.pdf

2024-09-20T09:15:25Z

Ivan Shilin:

Заглавная страница

2024-09-20T09:14:54Z

Ivan Shilin:

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==



* [https://www.hse.ru/our/news/876470885.html Интервью Юлия Сергеевича "Вышке для своих" (30 ноября 2023)]
* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==

* [http://www.dyn-sys.org/w/images/d/df/Ilyashenko_2024_stability.pdf "Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields"] by Yu. Ilyashenko, Journal of Fixed Point Theory and Applications, V. 26, article 24, 2024.
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

* Статья Диего М. Бенардета:

[https://www.tandfonline.com/doi/pdf/10.1080/00029890.2022.2005389 "Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model" by Diego M. Benardete (the paper expounds Yu. S. Ilyashenko's method of obtaining an upper bound on the number of limit cycles and applies this methos to a neural model)]

* Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса:
[http://www.dyn-sys.org/w/images/a/af/Ilyashenko_-_SelMathSov.pdf "Weakly Contracting Systems and Attractors of Galerkin Approximations of Navier-Stokes Equations on the Two-Dimensional Torus", 1992]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Файл:Ilyashenko 2024 stability.pdf

2024-09-20T09:06:41Z

Ivan Shilin: Статья Ю.С. Ильяшенко "Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields".

== Краткое описание ==
Статья Ю.С. Ильяшенко "Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields".

Заглавная страница

2023-12-05T21:02:56Z

Ivan Shilin: добавлена ссылка на интервью Юлия Сергеевича

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==



* [https://www.hse.ru/our/news/876470885.html Интервью Юлия Сергеевича "Вышке для своих" (30 ноября 2023)]
* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

* Статья Диего М. Бенардета:

[https://www.tandfonline.com/doi/pdf/10.1080/00029890.2022.2005389 "Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model" by Diego M. Benardete (the paper expounds Yu. S. Ilyashenko's method of obtaining an upper bound on the number of limit cycles and applies this methos to a neural model)]

* Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса:
[http://www.dyn-sys.org/w/images/a/af/Ilyashenko_-_SelMathSov.pdf "Weakly Contracting Systems and Attractors of Galerkin Approximations of Navier-Stokes Equations on the Two-Dimensional Torus", 1992]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Заглавная страница

2022-09-15T11:57:30Z

Ivan Shilin:

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==




* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

* Статья Диего М. Бенардета:

[https://www.tandfonline.com/doi/pdf/10.1080/00029890.2022.2005389 "Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model" by Diego M. Benardete (the paper expounds Yu. S. Ilyashenko's method of obtaining an upper bound on the number of limit cycles and applies this methos to a neural model)]

* Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса:
[http://www.dyn-sys.org/w/images/a/af/Ilyashenko_-_SelMathSov.pdf "Weakly Contracting Systems and Attractors of Galerkin Approximations of Navier-Stokes Equations on the Two-Dimensional Torus", 1992]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Файл:Ilyashenko - SelMathSov.pdf

2022-09-15T11:55:09Z

Ivan Shilin: Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса

Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса

Заглавная страница

2022-06-29T12:46:39Z

Ivan Shilin: added the paper by D. Benardete

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==




* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

[https://www.tandfonline.com/doi/pdf/10.1080/00029890.2022.2005389 "Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model" by Diego M. Benardete (the paper expounds Yu. S. Ilyashenko's method of obtaining an upper bound on the number of limit cycles and applies this methos to a neural model)]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Seminar talks 2020-2021

2021-10-29T21:22:08Z

Ivan Shilin: /* List of talks */

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

==Осень 2021==
* 29.10.21 Илья Андросов, «Глокальные бифуркации в типичных однопараметрических семействах на S2».
* 22.10.21 Ю.С. Ильяшенко, «Одновременная униформизация и квазиконформные отображения».
* 15.10.21 Ю.С. Ильяшенко, «Униформизация римановых поверхностей».
* 01.10.21 и 08.10.21 Г.Б. Шабат, «Римановы поверхности».
* 24.09.21 Андрей Дуков, «Седловые полициклы коразмерности 2».
* 17.09.21 Ю.С. Ильяшенко, «Нерешенные задачи и планы семинара».
* 10.09.21 Ю.С. Ильяшенко и А.А. Глуцюк, «Локальные задачи анализа и проблема различения центра и фокуса».

==Весна 2021==
* 14.05.21 и 21.05.21 Наташа Гончарук, «Что такое ренормализация».
* 23.04.21 и 30.04.21 Юрий Кудряшов, «Бифуркации векторных полей на плоскости».
* 16.04.21 Андрей Коняев (МГУ им. М. В. Ломоносова), «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/w/images/a/a1/Konyaev_160421.pdf Слайды.]
* 09.04.21 Станислав Минков, «Пересечение аттракторов и репеллеров и постоянные гетероклинические касания».
* 02.04.21 Phillipo Lappicy (Universidade de São Paulo), "Bifurcations and Chaos in Hořava-Lifshitz Cosmology".
* 19.03.21 Юлий Сергеевич Ильяшенко, «Большие носители».
* 12.03.21 Алексей Окунев, «Метод усреднения, прохождение через резонансы и сепаратрисы».
* 05.03.21 John Guckenheimer (Cornell University), "Principal Foliations".
* 26.02.21 Антон Городецкий (University of California Irvine), «Теорема Фюрстенберга и ее обобщения».
* 19.02.21 Алексей Глуцюк, «О семействах перемычек в модели перехода Джозефсона ... - 3: доказательства». [http://www.dyn-sys.org/w/images/b/b6/Glutsyuk_190221.pdf Слайды].
* 12.02.21 Алексей Клименко, «Философия общности положения. Лемма Сарда и теорема Тома» (Ликбез).
* 11.12.20 Виктор Клепцын, «Предельные объекты в теории случайных матриц с \beta=\infty».
* 04.12.20 Илья Мещихин и Станислав Минков, «Динамические системы и разработка протеза ноги».
* 27.11.20 Сергей Владимирович Гонченко, «О трёх типах динамики и динамического хаоса».
* 13.11.20 Илья Щуров, "История хаотической динамики".
* 06.11.20 Bertrand Deroin (CNRS – IMPA, Rio de Janeiro – AGM, Cergy-Pontoise), "Dynamics of Jouanolou foliation".
* Under construction

Заглавная страница

2021-10-29T21:13:58Z

Ivan Shilin: правка предыдущего

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==




* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

[http://www.dyn-sys.org/w/images/5/5c/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3_%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%B5%D0%BD%D1%82_%D0%BE_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%BE%D1%83%D0%B7%D0%BB%D0%B0_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D0%BA_%D0%BF%D0%B5%D1%82%D0%BB%D0%B5_%D1%81%D0%B5%D0%B4%D0%BB%D0%B0.pdf "О некоторых нелокальных двухпараметрических бифуркациях векторных полей на поверхностях, имеющих особую точку типа седлоузла седел" (фрагмент)]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Файл:Ройтенберг фрагмент о сепаратрисе седлоузла предельной к петле седла.pdf

2021-10-29T21:13:10Z

Ivan Shilin:

Заглавная страница

2021-10-29T21:06:55Z

Ivan Shilin: добавлены статьи В.Ш. Ройтенберга (с его разрешения)

[[/en|English version]]


<big>'''Dynamical Systems'''</big>

Welcome to the official site of the seminar on Dynamical Systems supervised by Yu.S.Ilyashenko.

The seminar on Dynamical Systems supervised now by A.Gorodetski and Yu. Ilyashenko continues the activities started 30 years ago in the seminar on Differential Equations organized by N. Nekhoroshev and Yu. Ilyashenko.

The modern theory of dynamical systems is one of the main tools of natural studies. As a mathematical discipline it spreads from physics and probability to multidimentional complex analysis and algebraic geometry.

Some key problems are: How chaos occurs in deterministic systems? Where is the boundary between differential equations and probability theory in the description of the limit behavior of dynamical systems? Is our Solar System stable? What the attractor of a typical dynamical system looks like? What are the characteristic features of the foliations of a complex plane by analytic curves? What may be said about the number and location of limit cycles of a planar polynomial vector field? These questions (two of them going back to Poincare and Hilbert) are or were in the realm of the investigations of the seminar.

One of the traditions of the seminar is a part of a general tradition of Moscow Mathematical School. It is involving young students in the creative work on the very early stage of their education. Several new results are obtained by the third and second year undergraduate students participating the seminar.
== Current activities ==




* [[Seminar talks 2020-2021]]
* [[Dynamical Systems 2019]]

== Papers ==
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

* Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):

[http://www.dyn-sys.org/w/images/c/c9/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84%D1%83%D1%80%D0%BA%D0%B0%D1%86%D0%B8%D1%8F%D1%85_%D1%81%D0%B5%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D1%80%D0%B8%D1%81_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D1%85_%D0%BA_%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D0%BE%D0%BC%D1%83_%D1%86%D0%B8%D0%BA%D0%BB%D1%83.pdf "О бифуркациях сепаратрис, предельных к двойному циклу", 1995]

[http://www.dyn-sys.org/w/images/c/cf/Roitenberg_thesis_2000.pdf "Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000]

[http://www.dyn-sys.org/w/images/4/42/%D0%A0%D0%BE%D0%B9%D1%82%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3._%D0%9E_%D0%B1%D0%B8%D1%84._%D0%B2.%D0%BF.%2C_%D0%B8%D0%BC%D0%B5%D1%8E%D1%89%D0%B8%D1%85_%D1%8F%D1%87%D0%B5%D0%B9%D0%BA%D1%83%2C_%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D0%BD%D0%BD%D1%83%D1%8E_%D0%B4%D0%B2._%D1%86%D0%B8%D0%BA%D0%BB%D0%B0%D0%BC%D0%B8.pdf "О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2008_7_58.pdf "О бифуркациях векторных полей, имеющих ячейки, состоящие из траекторий, предельных к двойным циклам", 2008]

[https://www.gramota.net/articles/issn_1993-5552_2012_7_34.pdf "О бифуркациях векторных полей, имеющих сепаратрису, предельную к контуру из сепаратрис двух разноплановых седел", 2012]

== Links ==
* [http://www.dyn-sys.org/w/images/5/5f/GlobifF.pdf Slides] of Yu. Ilyashenko's talk on global bifurcations {{ref-ru}}
* [http://www.dyn-sys.org/public/ODE-notes/ODE.pdf ODE textbook: Bufetov, Goncharuk, Ilyashenko] (September 2, 2019). Current status is described [http://www.dyn-sys.org/public/ODE-notes/Status.doc here].
* [[Plan:Fall 2013]] {{ref-ru}}
* [[I-Ya translation]] {{ref-ru}}
* [[Российская_газета_о_НМУ|Russian gazette about IUM]] {{ref-ru}}
* [[Grant numbers]]

Файл:Ройтенберг. О биф. в.п., имеющих ячейку, ограниченную дв. циклами.pdf

2021-10-29T20:58:53Z

Ivan Shilin:

Файл:Ройтенберг. О бифуркациях сепаратрис предельных к двойному циклу.pdf

2021-10-29T20:57:07Z

Ivan Shilin:

Файл:Roitenberg thesis 2000.pdf

2021-10-29T20:55:15Z

Ivan Shilin:

Seminar talks 2020-2021

2021-05-25T16:02:23Z

Ivan Shilin: /* List of talks */

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

* 14.05.21 и 21.05.21 Наташа Гончарук, «Что такое ренормализация».
* 23.04.21 и 30.04.21 Юрий Кудряшов, «Бифуркации векторных полей на плоскости».
* 16.04.21 Андрей Коняев (МГУ им. М. В. Ломоносова), «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/w/images/a/a1/Konyaev_160421.pdf Слайды.]
* 09.04.21 Станислав Минков, «Пересечение аттракторов и репеллеров и постоянные гетероклинические касания».
* 02.04.21 Phillipo Lappicy (Universidade de São Paulo), "Bifurcations and Chaos in Hořava-Lifshitz Cosmology".
* 19.03.21 Юлий Сергеевич Ильяшенко, «Большие носители».
* 12.03.21 Алексей Окунев, «Метод усреднения, прохождение через резонансы и сепаратрисы».
* 05.03.21 John Guckenheimer (Cornell University), "Principal Foliations".
* 26.02.21 Антон Городецкий (University of California Irvine), «Теорема Фюрстенберга и ее обобщения».
* 19.02.21 Алексей Глуцюк, «О семействах перемычек в модели перехода Джозефсона ... - 3: доказательства». [http://www.dyn-sys.org/w/images/b/b6/Glutsyuk_190221.pdf Слайды].
* 12.02.21 Алексей Клименко, «Философия общности положения. Лемма Сарда и теорема Тома» (Ликбез).
* 11.12.20 Виктор Клепцын, «Предельные объекты в теории случайных матриц с \beta=\infty».
* 04.12.20 Илья Мещихин и Станислав Минков, «Динамические системы и разработка протеза ноги».
* 27.11.20 Сергей Владимирович Гонченко, «О трёх типах динамики и динамического хаоса».
* 13.11.20 Илья Щуров, "История хаотической динамики".
* 06.11.20 Bertrand Deroin (CNRS – IMPA, Rio de Janeiro – AGM, Cergy-Pontoise), "Dynamics of Jouanolou foliation".
* Under construction

Seminar talks 2020-2021

2021-04-18T12:08:00Z

Ivan Shilin:

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

* 16.04.21 Андрей Коняев (МГУ им. М. В. Ломоносова), «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/w/images/a/a1/Konyaev_160421.pdf Слайды.]
* 09.04.21 Станислав Минков, «Пересечение аттракторов и репеллеров и постоянные гетероклинические касания».
* 02.04.21 Phillipo Lappicy (Universidade de São Paulo), "Bifurcations and Chaos in Hořava-Lifshitz Cosmology".
* 19.03.21 Юлий Сергеевич Ильяшенко, «Большие носители».
* 12.03.21 Алексей Окунев, «Метод усреднения, прохождение через резонансы и сепаратрисы».
* 05.03.21 John Guckenheimer (Cornell University), "Principal Foliations".
* 26.02.21 Антон Городецкий (University of California Irvine), «Теорема Фюрстенберга и ее обобщения».
* 19.02.21 Алексей Глуцюк, «О семействах перемычек в модели перехода Джозефсона ... - 3: доказательства». [http://www.dyn-sys.org/w/images/b/b6/Glutsyuk_190221.pdf Слайды].
* 12.02.21 Алексей Клименко, «Философия общности положения. Лемма Сарда и теорема Тома» (Ликбез).
* 11.12.20 Виктор Клепцын, «Предельные объекты в теории случайных матриц с \beta=\infty».
* 04.12.20 Илья Мещихин и Станислав Минков, «Динамические системы и разработка протеза ноги».
* 27.11.20 Сергей Владимирович Гонченко, «О трёх типах динамики и динамического хаоса».
* 13.11.20 Илья Щуров, "История хаотической динамики".
* 06.11.20 Bertrand Deroin (CNRS – IMPA, Rio de Janeiro – AGM, Cergy-Pontoise), "Dynamics of Jouanolou foliation".
* Under construction

Seminar talks 2020-2021

2021-04-18T12:00:22Z

Ivan Shilin:

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

* 16.04.21 Андрей Коняев (МГУ им. М. В. Ломоносова), «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/w/images/a/a1/Konyaev_160421.pdf Слайды.]
* 09.04.21 Станислав Минков, «Пересечение аттракторов и репеллеров и постоянные гетероклинические касания».
* 02.04.21 Phillipo Lappicy (Universidade de São Paulo), "Bifurcations and Chaos in Hořava-Lifshitz Cosmology".
* 19.03.21 Юлий Сергеевич Ильяшенко, «Большие носители».
* 12.03.21 Алексей Окунев, «Метод усреднения, прохождение через резонансы и сепаратрисы».
* 05.03.21 John Guckenheimer (Cornell University), "Principal Foliations".
* 26.02.21 Антон Городецкий (University of California Irvine), "Теорема Фюрстенберга и ее обобщения".
* 19.02.21 Алексей Глуцюк, "О семействах перемычек в модели перехода Джозефсона ... - 3: доказательства". [http://www.dyn-sys.org/w/images/b/b6/Glutsyuk_190221.pdf Слайды].
* 12.02.21 Алексей Клименко, «Философия общности положения. Лемма Сарда и теорема Тома» (Ликбез).
* 11.12.20 Виктор Клепцын, «Предельные объекты в теории случайных матриц с \beta=\infty».
* 04.12.20 Илья Мещихин и Станислав Минков, "Динамические системы и разработка протеза ноги".
* Under construction

Файл:Glutsyuk 190221.pdf

2021-04-18T11:57:20Z

Ivan Shilin: Слайды 3-го (в сезоне 20-21) доклада Алексея Глуцюка про эффект Джозефсона, 19.02.21.

Слайды 3-го (в сезоне 20-21) доклада Алексея Глуцюка про эффект Джозефсона, 19.02.21.

Seminar talks 2020-2021

2021-04-18T11:20:54Z

Ivan Shilin:

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

* 16.04.21 Аднрей Коняев (МГУ им. М. В. Ломоносова) «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/w/images/a/a1/Konyaev_160421.pdf Слайды.]
* Under construction

Seminar talks 2020-2021

2021-04-18T11:18:37Z

Ivan Shilin: Новая страница: « == [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] == == List of talks == * 16.04.21 Аднрей Коняев (…»

== [https://www.youtube.com/playlist?list=PLg3X2L31X9-PfQJ1nV1L8qMQkvTeoPbCi Playlist on YouTube] ==

== List of talks ==

* 16.04.21 Аднрей Коняев (МГУ им. М. В. Ломоносова) «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры». [http://www.dyn-sys.org/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Konyaev_160421.pdf Слайды.]
* Under construction

Файл:Konyaev 160421.pdf

2021-04-18T11:16:30Z

Ivan Shilin: Слайды доклада Андрея Коняева «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры».

Слайды доклада Андрея Коняева «Задача линеаризации для операторов Нийенхейса и левосимметрические алгебры».

Заглавная страница

2021-04-18T11:06:40Z

Ivan Shilin:

Заглавная страница

2021-01-05T14:11:32Z

Ivan Shilin:

Papers

2021-01-05T14:10:42Z

Ivan Shilin:

=== Bifurcations ===
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"] by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742 https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]

[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]

[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.] [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]

=== Foliations ===
* Alexey Glutsyuk and Mikhail Lyubich. [http://wiki.dynsys.org/misc/uerghyp.pdf Unique ergodicity of horospheric foliations revisited].
* B. Deroin, V. Kleptsyn, [http://arxiv.org/abs/math/0506204 Random conformal dynamical systems], ''Geometry and Functional Analysis'', '''17''' (2007), no. 4, pp. 1043-1105.
===== Foliations in complex plane =====
* D. Volk, [http://dx.doi.org/10.1134%2FS0081543806030072 The density of separatrix connections in the space of polynomial foliations in <math>\mathbb{C}P^2</math>], ''Proceedings of the Steklov Institute of Mathematics'' (2006), vol. 254, pp. 169-179 (Рус.: [http://denisvolk.com/math/ru/papers/seplink.pdf Плотность сепаратрисных связок в пространстве полиномиальных слоений в <math>\mathbb{C}P^2</math>], Нелинейные аналитические дифференциальные уравнения, Сборник статей, Тр. МИАН, 254, Наука, М., 2006, 181–191)
* T. Golenishcheva-Kutuzova, V. Kleptsyn, Minimality and ergodicity of a generic analytic foliation of <math>\mathbb{C}^2</math>, ''Ergodic Theory and Dynamical Systems'', '''28''' (2008), no. 5, pp. 1533--1544.

=== Attractors & time averages ===
===== Thick attractors =====
* Yu. Ilyashenko, Thick Attractors of Step Skew Products, ''Regular and Chaotic Dynamics'', Vol. '''15''', Nos. 2-3, pp. 328-334

* D. Volk, [http://arxiv.org/abs/1108.5330 Persistent massive attractors of smooth maps], arXiv:1108.5330

===== Invisible attractors =====
* Yu. Ilyashenko, A. Negut, [http://dyn-sys.org/misc/NON-IN-final.pdf Invisible parts of attractors]. ''Nonlinearity'', '''23''' (2010) 1199—1219. [http://stacks.iop.org/Non/23/1199]
* Yu. Ilyashenko, D. Volk, [http://denisvolk.com/math/en/papers/cascad_edit.pdf Cascades of <math>\varepsilon</math>-invisibility], ''Journal of Fixed Point Theory and Applications'', '''7''', 2010, 161--188 (Рус.: [http://denisvolk.com/math/ru/papers/cascad_rus.pdf Каскады <math>\varepsilon</math>-невидимости])

===== Other examples of pathological attractors =====
* V. Kleptsyn, An example of non-coincidence of minimal and statistical attractors, ''Ergodic Theory and Dynamical Systems'', '''26''' (2006), no. 3, pp. 759-768.
* T. Golenishcheva-Kutuzova, V. Kleptsyn, Non-convergence of the Krylov-Bogolubov procedure for the Bowen's example, ''Mathematical Notes'', '''82''' (2007), no. 5, pp. 678—689.
===== Ittai Kan example =====
* Yu. Ilyashenko, V. Kleptsyn, P. Saltykov, Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins. ''Journal of Fixed Point Theory and Applications'', '''3''' (2008), no. 2, pp. 449--463.

===== Special Ergodic Theorem =====
* V. Kleptsyn, D. Ryzhov, [http://arxiv.org/abs/1109.4060 Special Ergodic Theorem for hyperbolic maps], arXiv:1109.4060

=== Lyapunov exponents ===
* A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, [http://mi.mathnet.ru/rus/faa/v39/i1/p27 Nonremovable Zero Lyapunov Exponents], ''Funkts. Anal. Prilozh.'', '''39''':1 (2005), 27–38
* V. Kleptsyn, M. Nalski, Stability of existence of non-hyperbolic measures for C¹-diffeomorphisms, ''Functional Analysis and its Applications'', '''41''' (2007), no. 4, pp. 271--283.

=== One-dimensional dynamics ===
* B. Deroin, V. Kleptsyn, A. Navas, [http://arxiv.org/abs/math/0506063 Sur la dynamique unidimensionelle et régularité intermédiaire], preprint IHES M/05/24, ''Acta Mathematica'', '''199''' (2007), pp. 199--262.
* V. Kleptsyn, A. Navas, [http://arxiv.org/abs/0704.1006 A Denjoy type theorem for commuting circle diffeomorphisms with derivatives having different Hölder differentiability classes], ''Moscow Math. Journal'' '''8''' (2008), no. 3, 477-492, 616.
* B. Deroin, V. Kleptsyn, A. Navas, [http://arxiv.org/abs/0806.1974 On the question of ergodicity for minimal group actions on the circle], ''Moscow Math. Journal'', '''9''' (2009), no. 2, pp. 263--303.

=== Slow-fast systems ===
* I. V. Schurov. [http://dx.doi.org/10.1007/s10883-010-9093-9 ''Ducks On The Torus: Existence and Uniqueness'']. Journal of Dynamical and Control Systems, '''16''':2 (2010), 267—300. Preprint: [http://arxiv.org/abs/0910.1888 arXiv:0910.1888v1 (math.DS)]
* Щуров И.В. [http://dyn-sys.org/public/ducks-nonconvex-trudy.pdf ''Уточные циклы в типичных быстро-медленных системах на торе.''], Труды ММО '''71''' (2010), 200-234
** Translation: I. V. Shchurov. ''[http://www.ams.org/journals/mosc/2010-71-00/S0077-1554-2010-00184-7/home.html Canard cycles in generic fast-slow systems on the torus.]'' Transactions of the Moscow Mathematical Society, '''2010''', 175-207 [http://www.dyn-sys.org/public/ducks-nonconvex-trudy-en.pdf PDF]
* I. V. Schurov. ''Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems'', submitted to the proceedings for the Eighth AIMS International Conference on Dynamical Systems, Differential Equations and Applications, [http://arxiv.org/abs/1008.0133 arXiv:1008.0133 (Math.DS)].

=== Limit cycles ===
* P. Kaleda, I. Schurov. ''Cyclicity of Elementary Polycycles with Fixed Singular Points Number in Generic k-Parametric Families''. ''Algebra and Analysis'' (''St. Petersburg Mathematical Journal'') (Рус.: П. И. Каледа, И. В. Щуров. [http://www.dyn-sys.org/public/kaleda-schurov-HA.pdf «Цикличность элементарных полициклов с фиксированным числом особых точек в типичных k-параметрических семействах»]. Алгебра и анализ. '''22''':4 (2010), 57—75)

=== Periodic orbits ===
* A. Glutsyk, Yu. Kudryashov. [http://www.dyn-sys.org/files/bill-jmd.pdf "No planar billiard possesses an open set of quadrilateral trajectories"], submitted to [http://www.math.psu.edu/jmd/ Journal of Modern Dynamics].

Заглавная страница

2021-01-05T13:56:44Z

Ivan Shilin:

Grant numbers

2021-01-05T11:56:49Z

Ivan Shilin:

Currently the following Seminar's grants are active:

* RFBR project 20-01-00420-a
* Grant No 16-05-0066 supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.

Please, cite the latter grant (if applicable) as follows:

The article was prepared within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2016-2017 (grant No 16-05-0066) and supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program

Заглавная страница

2021-01-05T10:53:29Z

Ivan Shilin:

Файл:CHA20-AR-GBC2021-01328.pdf

2021-01-05T10:43:32Z

Ivan Shilin: Статья Юлия Сергеевича про SN-SN; принято

Статья Юлия Сергеевича про SN-SN; принято

Заглавная страница

2020-10-23T16:06:47Z

Ivan Shilin:

Заглавная страница

2020-10-23T15:29:59Z

Ivan Shilin:

Файл:GIS parabolic cycle.pdf

2020-10-23T15:18:06Z

Ivan Shilin:

Файл:IS saddle loop.pdf

2020-10-23T15:17:48Z

Ivan Shilin:

Файл:Starichkova tame 1 par families.pdf

2020-10-23T15:14:07Z

Ivan Shilin:

Заглавная страница

2020-09-24T16:18:58Z

Ivan Shilin: Выложена статья про ростки биф. диаграмм.

Файл:GermsBD.pdf

2020-09-24T16:12:38Z

Ivan Shilin:

Файл:GlobifF.pdf

2020-05-13T10:34:39Z

Ivan Shilin: Ivan Shilin загружена новая версия «Файл:GlobifF.pdf»

Слайды доклада Ю.С. Ильяшенко "Глобальная теория бифуркаций на плоскости"

Заглавная страница

2020-05-03T15:58:57Z

Ivan Shilin:

Файл:GlobifF.pdf

2020-05-03T15:45:04Z

Ivan Shilin: Слайды доклада Ю.С. Ильяшенко "Глобальная теория бифуркаций на плоскости"

Слайды доклада Ю.С. Ильяшенко "Глобальная теория бифуркаций на плоскости"

Summer School 2016

2016-07-11T12:27:13Z

Ivan Shilin: добавлен список лекций на русском

{{Lifr-header}}

'''Summer School on Dynamical Systems — 2016''' under supervision of Yulij Ilyashenko will take place in Ratmino (Dubna, Russia) in June 29 — July 9, 2016.

== Organizers ==
The school is organized by [http://mccme.ru Moscow Center of Continuous Mathematical Education] and [http://poncelet.ru/ Laboratoire J.-V.Poncelet].

Organizing Committee:
* Yulij Ilyashenko
* Yury Kudryashov
* Stanislav Minkov
* Ivan Shilin
* Ilya Schurov
* Ivan Yaschenko

Program Committee:
* Yulij Ilyashenko
* Michael Tsfasman

Contact: ischurov (at) hse.ru.

== Лекции ==
=== Лекции Ю.С. Ильяшенко===
# Структурная устойчивость и бифуркации в однопараметрических семействах
# Графы Майера систем Морса-Смейла
# Графы Майера общих и квазиобщих систем
# Простые бифуркации в однопараметрических семействах
# Бифуркации полей класса SL (совм. с В. Старичковой)
# Большие носители (совм. с Н. Гончарук)
# Бифуркации параболических циклов (совм. с Н. Солодовниковым)
# Числовые и функциональные инварианты (совм. с Ю. Кудряшовым)
# Сага о параболических ростах (совм. с Б. Шлейфманом)

=== Лекции и миникурсы других участников ===
* В. А. Клепцын "Действия групп на окружности", "Нестационарное облако точек", "Теорема Фюрстенберга с параметром"
* Т. С. Фирсова "Ежик в <math>\mathbb{C}^2</math>"
* Д. И. Зубов "Трансверсальные меры систем Аносова"
* А. В. Окунев "Сингулярность стационарной меры"
* И. С. Шилин "Расщепление с доминированием или неустойчивость"
* Н. Б. Гончарук "Большие носители"
* С. С. Минков "Невероятный диффеоморфизм Аносова"
* И. В. Щуров "Многообходные утки на торе"
* А. В. Дуков "Полицикл Сердце"
* Д. А. Голубенко "Вертексные алгебры"

Bifurcations 2015

2015-04-13T18:34:28Z

Ivan Shilin:

Спецкурс Ю.С. Ильяшенко «Теория бифуркаций», весна 2014-15 учебного года.

* [https://drive.google.com/file/d/0B9DJ1_g-WKm1Rk9RbDB5M2lSSGM/view?usp=sharing Черновик обзора глобальных бифуркаций на плоскости (выложен 10.04.15)]

* [https://www.youtube.com/channel/UCiuIWkZAXNteFruoL7MsIOw Видеозаписи лекций]

Архив курсов

2015-04-10T11:25:09Z

Ivan Shilin:

== 2014-15 ==
* [[Bifurcations_2015 | Теория бифуркаций]] (Ю. С. Ильяшенко)

== 2013-14 ==
* [[Limit_Cycles_2014 | Теоремы конечности 2]] (Ю. С. Ильяшенко)

== 2012-13 ==
* [[Семинар в НМУ 2012-13|Курс-семинар в НМУ]] (И. В. Щуров, В. А. Клепцын)
* [[Просеминар 2012-13]]
* [http://math-hse.info/2012-13/ODE?uselang=en Ordinary differential equations] in Math in Moscow (D. A. Filimonov, I. V. Schurov, A. P. Pushkar).

== 2011-12 ==
* [[Курсы в МГУ/Просеминар 2011|Просеминар 2011-12]] (А. И. Буфетов, Н. Б. Гончарук, О. Л. Ромаскевич)
* [[Курсы в МГУ/ОДУ осень 2011|Обыкновенные дифференциальные уравнения]] (А. И. Буфетов, Ю. С. Ильяшенко)
== 2010-11 ==
* [[MIM/2010-spring|Ordinary differential equations]] in Math in Moscow.

== 2008-2009 ==
* [[Ликбез 2008]] (Денис Волк, Виктор Клепцын, Алексей Глуцюк)
== 2007-2008 ==
* [[Динамические системы (осень 2007)]] (Аносов Д.В., Клименко А.В. и Колюцкий Г.А.)

Bifurcations 2015

2015-04-10T11:24:49Z

Ivan Shilin: Новая страница: «Спецкурс Ю.С. Ильяшенко «Теория бифуркаций», весна 2014-15 учебного года. * [https://drive.google.com/file/…»

Plan:Fall 2014

2014-07-17T15:23:02Z

Ivan Shilin:

Планы '''семинара в МГУ''' по пятницам (18:25, ауд. 1414), осень 2014.

Вы можете вписать себя в эту табличку [http://www.dyn-sys.org/w/index.php?title=Plan:Fall_2014&action=edit самостоятельно]. Вписывайте свое имя и название доклада вместо «???». После этого можно перейти по «красной ссылке» с названием доклада, и заполнить аннотацию. Аннотации имеет смысл заполнять сильно заранее — это поможет и при организации рассылки.

Программа носит '''очень предварительный''' характер.

{| class='wikitable'
! дата || докладчик(и) || тема || комментарии
|-
| 5.9 || Ольга Ромаскевич || [[Доклад:5.9.2014| ??? ]] ||
|-
| 12.9 || Алексей Глуцюк || [[Доклад:12.9.2014| ??? ]] ||
|-
| 19.9 || Юрий Кудряшов, Наталия Гончарук || [[Доклад:19.9.2014| ??? ]] ||
|-
| 26.9 || Алексей Окунев || [[Доклад:26.9.2014| ??? ]] ||
|-
| 3.10 || ??? || [[Доклад:3.10.2014| ??? ]] ||
|-
| 10.10 || ??? || [[Доклад:10.10.2014| ??? ]] ||
|-
| 17.10 || ??? || [[Доклад:17.10.2013| ??? ]] ||
|-
| 24.10 || ??? || [[Доклад:24.10.2013| ??? ]] ||
|}

== Запланированные доклады без конкретной даты ==
* Юрий Кудряшов и Наталия Гончарук, Обзор теории слоений
* Юрий Кудряшов и Наталия Гончарук, О многих ручках и циклах
* Юрий Кудряшов, Голономия в гиперболических слоениях
* Илья Щуров, Проблема Гильберта-Арнольда
* Станислав Минков, Толстые аттракторы
* Станислав Минков, Превалентность
* Борис Шлейфман, Граф потока на сфере
* Андрей Дуков, Бифуркация Богданова -- Такенса
* Андрей Солоницын, Нелокальные бифуркации (гл. 4-5)
* ??? Равновесные меры (совет Вити Клепцына)

Limit Cycles 2014

2014-05-14T20:07:17Z

Ivan Shilin:

Спецкурс Ю.С. Ильяшенко «Теоремы конечности для предельных циклов 2», весна 2013-14 учебного года.

* [http://www.dyn-sys.org/w/images/4/4c/Main.pdf Главы 0-3 (обновлены 14.05.14)]

* [http://yadi.sk/d/cr4TQ40KJDeZY Видеозаписи (первых двух) лекций на яндекс.диске]

* [http://www.mathnet.ru/php/conference.phtml?eventID=12&confid=523&option_lang=rus&if_videolibrary=1 Видеозапись курса на матнете]

Файл:Main.pdf

2014-05-14T20:00:27Z

Ivan Shilin: Ivan Shilin загружена новая версия «Файл:Main.pdf»

Limit Cycles 2014

2014-04-30T15:15:38Z

Ivan Shilin:

Спецкурс Ю.С. Ильяшенко «Теоремы конечности для предельных циклов 2», весна 2013-14 учебного года.

* [http://www.dyn-sys.org/w/images/4/4c/Main.pdf Главы 0-3 (обновлены 30.04.14)]

* [http://yadi.sk/d/cr4TQ40KJDeZY Видеозаписи (первых двух) лекций на яндекс.диске]

* [http://www.mathnet.ru/php/conference.phtml?eventID=12&confid=523&option_lang=rus&if_videolibrary=1 Видеозапись курса на матнете]

Файл:Main.pdf

2014-04-30T14:47:01Z

Ivan Shilin: Ivan Shilin загружена новая версия «Файл:Main.pdf»

Limit Cycles 2014

2014-04-03T17:27:49Z

Ivan Shilin:

Спецкурс Ю.С. Ильяшенко «Теоремы конечности для предельных циклов 2», весна 2013-14 учебного года.

* [http://www.dyn-sys.org/w/images/4/4c/Main.pdf Главы 0-2 (обновлены 03.04.14)]

* [http://yadi.sk/d/cr4TQ40KJDeZY Видеозаписи (первых двух) лекций на яндекс.диске]

* [http://www.mathnet.ru/php/conference.phtml?eventID=12&confid=523&option_lang=rus&if_videolibrary=1 Видеозапись курса на матнете]

Файл:Main.pdf

2014-04-03T17:16:24Z

Ivan Shilin: Ivan Shilin загружена новая версия «Файл:Main.pdf»