Seminars
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  


Course by O. È. Zubelevich "Elements of Dynamical Systems"
September 11–December 18, 2023, Steklov Mathematical Institute, Room 430 (8 Gubkina)

We kindly ask all participants, including remote ones and those
watching recorded videos, to register at this link.


The aim of the lecture course is to show the diversity of problems and methods of dynamical systems. The lecture course consists of several independent topics. We consider finite and infinite-dimensional dynamical systems and discuss the classical results as well as the results obtained in the last twenty years.

  1.  Dynamical systems with discrete time: the Poincare mapping at an energy level in a Hamiltonian system; other examples. Invariant measure, the ergodic theorems of Yosida, von Neumann, and Birkhoff. The Poincare recurrence theorem. Introduction to ergodic systems: basic theorems, the Koopman operator. Ergodicity of the tent map, ergodicity of the shift in the torus.
  2.  Other causes of the dynamical chaos’ appearance: separatrix splitting. The Poincare-Melnikov integral.
  3.  Discrete Lagrangian systems: the anti-integrable limit.
  4.  Time averaging in another context: an infinite-dimensional version of the Massera theorem and its application to elasticity theory.
  5.  Bounded solutions to the systems of the second order ODE.
  6.  A phase flow of an ODE with a smooth right-hand side: w—limit set and its properties, attractors.
  7.  ODE with discontinuous right-hand side, differential inclusions Filippov’s regularization, periodic solutions to systems with dry friction.

References
[1] V. Arnold, Ordinary Differential Equations. Springer, 1992.
[2] R. Temam, Infinite-dimensional dynamical systems. Springer, 1993.
[3] D. Treschev, O. Zubelevich, Introduction to the Perturbation Theory of Hamiltonian Systems. Springer, 2010.
[4] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, Transaction of A.M.S., 42 (1964), pp. 199-231.

Program

Lecturer
Zubelevich Oleg Èduardovich

Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no.  075-15-2022-265).



Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by O. È. Zubelevich "Elements of Dynamical Systems", September 11–December 18, 2023

December 4, 2023 (Mon)
1. Lecture 11. Elements of Dynamical Systems
O. È. Zubelevich
December 4, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

November 27, 2023 (Mon)
2. Lecture 10. Elements of Dynamical Systems
O. È. Zubelevich
November 27, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

November 20, 2023 (Mon)
3. Lecture 9. Elements of Dynamical Systems
O. È. Zubelevich
November 20, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

November 13, 2023 (Mon)
4. Lecture 8. Elements of Dynamical Systems
O. È. Zubelevich
November 13, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

October 30, 2023 (Mon)
5. Lecture 7. Elements of Dynamical Systems
O. È. Zubelevich
October 30, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

October 16, 2023 (Mon)
6. Lecture 6. Elements of Dynamical Systems
O. È. Zubelevich
October 16, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

October 9, 2023 (Mon)
7. Lecture 5. Elements of Dynamical Systems
O. È. Zubelevich
October 9, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

October 2, 2023 (Mon)
8. Lecture 4. Elements of Dynamical Systems
O. È. Zubelevich
October 2, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

September 25, 2023 (Mon)
9. Lecture 3. Elements of Dynamical Systems
O. È. Zubelevich
September 25, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

September 18, 2023 (Mon)
10. Lecture 2. Elements of Dynamical Systems
O. È. Zubelevich
September 18, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  

September 11, 2023 (Mon)
11. Lecture 1. Elements of Dynamical Systems
O. È. Zubelevich
September 11, 2023 18:00, Steklov Mathematical Institute, Room 430 (8 Gubkina)
O. È. Zubelevich
  
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024