2024/2025
Эргодическая теория
Статус:
Маго-лего
Кто читает:
Кафедра фундаментальной математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Малкин Михаил Иосифович
Язык:
русский
Кредиты:
6
Программа дисциплины
Аннотация
The course “Ergodic Theory” is aimed for introducing the students to the modern state and problems of dynamical systems having complicated (chaotic) behavior. Such systems usually can be described and studied with the help of Ergodic Theory.
Цель освоения дисциплины
- To show the actual state of studying complicated dynamical systems using invariant measures and dynamical invariants which are responsible for complexity of the system. To explain the phenomena of limit behavior of chaotic systems and its relation to the evolution limits of probability distributions in ergodic theorems ( the results going back to the results of Poincare, Birkhoff, , Khinchin, Krylov, Bogolyubov, Kolmogorov, Sinai). To provide constructions and methods for modeling invariant measures and computing the invariants for concrete dynamical systems..
Планируемые результаты обучения
- Knowledge of classical Ergodic theorems
- Understanding the constructions of invariant measures
- Understanding the constructions of Symbolic Dynamics.
- Understanding the relationship between topological dynamics and Ergodic Theory.
- Understanding the relationship between topological dynamics and Ergodic Theory.
Содержание учебной дисциплины
- Symbolic Dynamics
- Entropic Theory of Discrete Dynamical Systems.
- Classical Theorems of Ergodic Theory. Ergodic Theory of Low Dimensional Systems.
Промежуточная аттестация
- 2024/2025 4th module0.3 * Домашнее задание + 0.3 * Домашнее задание + 0.4 * Экзамен
Список литературы
Рекомендуемая основная литература
- Hasselblatt, Boris. Ergodic Theory and Negative Curvature [Электронный ресурс] / Boris Hasselblatt; БД springer. - Springer, Cham, 2017 - ISBN: 978-3-319-43058-4 (Print).
Рекомендуемая дополнительная литература
- . Kuznetsov, Sergey. Strange Nonchaotic Attractors : Dynamics Between Order and Chaos in Qua-siperiodically Forced Systems [Электронный ресурс] / Sergey Kuznetsov, Arkady Pikovsky, and Ul-rike Feudel. – World Scientific Publishing Co Pte Ltd, 2014, . – ISBN: 9789812566331 (Print).