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.
Lecturer
Date
10th September ~ 10th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-201 | ZOOM 14 | 712 322 9571 | BIMSA |
Syllabus
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
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.