Dynamical Systems seminar is supported by RFBR project 20-01-00420-a and Laboratory Poncelet.

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=== Bifurcations ===
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* [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]
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* Papers on global bifurcations in one-parameter families:
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[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.]
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[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.]
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[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)]
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=== Foliations ===  
 
=== Foliations ===  
 
* Alexey Glutsyuk and Mikhail Lyubich. [http://wiki.dynsys.org/misc/uerghyp.pdf Unique ergodicity of horospheric foliations revisited].
 
* Alexey Glutsyuk and Mikhail Lyubich. [http://wiki.dynsys.org/misc/uerghyp.pdf Unique ergodicity of horospheric foliations revisited].

Текущая версия на 07:10, 5 января 2021


Bifurcations

"Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.

"Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.

"Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov. (arXiv:1707.09779)

Foliations

Foliations in complex plane

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
Invisible attractors
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


Lyapunov exponents

  • A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, 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

Slow-fast systems

Limit cycles

Periodic orbits