Dynamical Systems seminar is supported by RFBR project 20-01-00420-a and Laboratory Poncelet.
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Dynamical Systems
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
- Интервью Юлия Сергеевича "Вышке для своих" (30 ноября 2023)
- Seminar talks 2020-2021
- Dynamical Systems 2019
Papers
- "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.
- "Dulac maps of real saddle-nodes" by Yu. Ilyashenko, Nonlinearity, V. 37, No. 10, 2024.
- "Germs of bifurcation diagrams and SN-SN families" by Yu. Ilyashenko, Chaos 31, 1, 2021, https://doi.org/10.1063/5.0030742
- Papers on global bifurcations in one-parameter families:
"Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.
"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)
- Papers on global bifurcations by V. Sh. Roitenberg (with his permission, in Russian):
"О бифуркациях сепаратрис, предельных к двойному циклу", 1995
"Нелокальные двухпараметрические бифуркации векторных полей на поверхностях", 2000
"О бифуркациях векторных полей, имеющих ячейку, ограниченную двойными циклами", 2008
- Статья Диего М. Бенардета:
- Статья Ю. С. Ильяшенко про аттракторы галёркинских приближений уравнения Навье-Стокса:
Links
- Slides of Yu. Ilyashenko's talk on global bifurcations (Russian)
- ODE textbook: Bufetov, Goncharuk, Ilyashenko (September 2, 2019). Current status is described here.
- Plan:Fall 2013 (Russian)
- I-Ya translation (Russian)
- Russian gazette about IUM (Russian)
- Grant numbers
