2026/2027
Современная теория динамических систем
Статус:
Маго-лего
Кто читает:
Кафедра фундаментальной математики
Охват аудитории:
для своего кампуса
Преподаватели:
Сафонов Клим Андреевич
Язык:
русский
Кредиты:
6
Контактные часы:
60
Программа дисциплины
Аннотация
The course is devoted to the description of the current state of the Theory of dynamic systems from the point of view of topological classification of important classes of systems with regular and chaotic dynamics.
Цель освоения дисциплины
- To show the current state of research in the field of discrete dynamical systems
- To introduce basic concepts of discrete dynamical systems
Планируемые результаты обучения
- The student reproduces basic definitions and statements given in the course
- The student explains the relationship between concepts and the roles of conditions in statements
- The student solves standard tasks, including proving simple statements
- The student proves non-trivial theorems
Содержание учебной дисциплины
- Discrete dynamical systems and their invariant sets
- One-dimensional dynamics
- Diffeomorphisms on surfaces. Appearance of chaos.
- Multidimensional dynamics
Список литературы
Рекомендуемая основная литература
- Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
- Grines V., Medvedev Timur, Pochinka O. Dynamical Systems on 2- and 3-Manifolds. Switzerland : Springer, 2016.
Рекомендуемая дополнительная литература
- Introduction to the modern theory of dynamical systems, Katok, A., 1999
- Katok, A. B., & Hasselblatt, B. (2002). Handbook of Dynamical Systems (Vol. 1st ed). Amsterdam: North Holland. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=207259