Equilibrium States and Ergodic Theory for Hyperbolic Dynamical Systems
This course explores the statistical and ergodic properties of hyperbolic dynamical systems through the framework of equilibrium states, a fundamental concept in modern smooth ergodic theory. Building on Rufus Bowen's seminal monograph, the course systematically develops the thermodynamic formalism for Anosov systems, establishing connections between dynamical invariants, ergodic theory, and statistical mechanics.
讲师
日期
2025年09月10日 至 12月10日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:55 | A3-3-201 | ZOOM 14 | 712 322 9571 | BIMSA |
课程大纲
1. Introduction
2. Gibbs Measures (Ruelle's Perron–Frobenius Theorem and the Variational Principle)
3. General Thermodynamic Formalism
4. Introduction to Hyperbolic Dynamics
5. Markov Partitions and Symbolic Dynamics
6. Ergodic Theory of Axiom A Diffeomorphisms
7. Statistical Properties of Smooth Expanding Maps
8. Piecewise Expanding Maps
2. Gibbs Measures (Ruelle's Perron–Frobenius Theorem and the Variational Principle)
3. General Thermodynamic Formalism
4. Introduction to Hyperbolic Dynamics
5. Markov Partitions and Symbolic Dynamics
6. Ergodic Theory of Axiom A Diffeomorphisms
7. Statistical Properties of Smooth Expanding Maps
8. Piecewise Expanding Maps
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。