Instructor: Maciej Zworski

Lectures: TuTh 2:10-3:30pm, Room 2 Evans

Course Control Number: 31369

Office: 801 Evans

Office Hours: Tu 1-2pm, or by appointment

Prerequisites: Firm background in real and complex analysis: Math 202AB; some basic knowledge of differential geometry;

Text: Yves Coudéne Ergodic Theory and Dynamical Systems (available via UC Berkeley Library Proxy)

Recommended Reading: On-line lecture notes by F. Rezakhanlou and by S. Nonnenmacher, and (for completely integrable systems) Notes on Dynamical Systems by J. Moser and E. Zehnder.

Syllabus: The course provides an introduction to dynamical systems with an emphasis on Hamiltonian systems and chaotic dynamics. Topics will include:

1. Ergodicity and mixing; recurrence

2. Hopf's argument for ergodicity

3. Case study: geodesics and horocyclic flows on constant curvature surfaces

4. Topological dynamics

5. Complete integrability, Liouville-Arnold theorem

6. Examples of integrable systems and Lax pairs: Toda lattice and QR algorithm

7. Topological and metric entropies, Lyapounov exponents.

Grading: The grade will be based on bi-weekly homework assignments.

Here are some notes on basic symplectic geometry. We will needs some of this material for the study of completely integrable systems.

A simple MATLAB code todam.m which provides an illustration for the Toda lattice evolution (type "help todam" in MATLAB to see how to use it).