Магистратура
2024/2025
Современная теория динамических систем
Статус:
Курс обязательный (Математика)
Направление:
01.04.01. Математика
Кто читает:
Кафедра фундаментальной математики
Когда читается:
1-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
6
Контактные часы:
56
Course Syllabus
Abstract
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.
Learning Objectives
- To show the current state of research in the field of discrete dynamical systems
- To introduce basic concepts of discrete dynamical systems
Expected Learning Outcomes
- 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
Course Contents
- Discrete dynamical systems and their invariant sets
- One-dimensional dynamics
- Diffeomorphisms on surfaces. Appearance of chaos.
- Multidimensional dynamics
Bibliography
Recommended Core Bibliography
- 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.
Recommended Additional Bibliography
- 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