Introduction to Ergodic theory
Ergodic theory studies statistical properties of deterministic dynamical systems. It can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. This course introduces the fundamental concepts of ergodic theory and its connections with dynamical systems. It includes topics on measure-preserving transformation, Ergodic Theorem, measure-theoretic entropy and topological entropy.
讲师
日期
2025年02月26日 至 06月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 09:50 - 12:15 | A3-3-201 | ZOOM 14 | 712 322 9571 | BIMSA |
修课要求
Basic knowledge of measure theory
课程大纲
1.Measure-Preserving Transformations;
2.Entropy;
3.Topological Dynamics;
4.Invariant Measures for Continuous Transformations;
5.Topological Entropy；
6.Relationship Between Topological Entropy and Measure-Theoretic Entropy.
2.Entropy;
3.Topological Dynamics;
4.Invariant Measures for Continuous Transformations;
5.Topological Entropy；
6.Relationship Between Topological Entropy and Measure-Theoretic Entropy.
参考资料
1. Peter Walters: An introduction to ergodic theory, Springer-Verlag, 1982.
2. Ricardo Mane: Ergodic theory and differentiable dynamics, Springer-Verlag, 1987.
3. Omri Sarig, Lecture Notes on Ergodic Theory.
4. 孙文祥:《遍历论》北京大学出版社, 2012.
2. Ricardo Mane: Ergodic theory and differentiable dynamics, Springer-Verlag, 1987.
3. Omri Sarig, Lecture Notes on Ergodic Theory.
4. 孙文祥:《遍历论》北京大学出版社, 2012.
听众
Advanced Undergraduate
, Graduate
视频公开
公开
笔记公开
不公开
语言
中文
讲师介绍
刘思序于2019年获得北京大学博士学位，之后在清华大学任博士后，并于2022年加入BIMSA任助理研究员。主要研究方向为动力系统与遍历论，统计试验设计。