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.
Lecturer
Date
6th March ~ 24th May, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-201 | ZOOM 02 | 518 868 7656 | BIMSA |
Prerequisite
Basic knowledge of measure theory
Syllabus
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.
Reference
1. Peter Walters: An introduction to ergodic theory, Springer-Verlag, 1982.
2. Ricardo Mane: Ergodic theory and differentiable dynamics, Springer-Verlag, 1987.
3. Rick Durrett: Probability--theory and examples(Fifth edition), Cambridge University Press, Cambridge, 2019.
4. Omri Sarig, Lecture Notes on Ergodic Theory.
5. 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. Rick Durrett: Probability--theory and examples(Fifth edition), Cambridge University Press, Cambridge, 2019.
4. Omri Sarig, Lecture Notes on Ergodic Theory.
5. 孙文祥:《遍历论》北京大学出版社, 2012.
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
Chinese
Lecturer Intro
Sixu Liu received her Ph.D. degree from Peking University in 2019. She then worked as a postdoc at Tsinghua University before joining BIMSA as an assistant professor in 2022. Her main research interests include dynamical systems and ergodic theory, as well as statistical experimental design.