Магистратура
2022/2023
Эргодическая теория
Статус:
Курс обязательный (Математика)
Направление:
01.04.01. Математика
Кто читает:
Кафедра фундаментальной математики
Когда читается:
1-й курс, 3, 4 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Малкин Михаил Иосифович
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
6
Контактные часы:
84
Course Syllabus
Abstract
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.
Learning Objectives
- 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..
Expected Learning Outcomes
- 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.
Course Contents
- Symbolic Dynamics
- Entropic Theory of Discrete Dynamical Systems.
- Classical Theorems of Ergodic Theory. Ergodic Theory of Low Dimensional Systems.
Bibliography
Recommended Core Bibliography
- Hasselblatt, Boris. Ergodic Theory and Negative Curvature [Электронный ресурс] / Boris Hasselblatt; БД springer. - Springer, Cham, 2017 - ISBN: 978-3-319-43058-4 (Print).
Recommended Additional Bibliography
- . 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).