Math 219 Dynamical Systems

Instructor: Maciej Zworski

Lectures: TuTh 11-12:30pm, Room 5 Evans

Course Control Number: 54401

Office: 801 Evans

Office Hours: Tu 2:10-3:30pm

Prerequisites: Firm background in real and complex analysis: Math 202AB

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. Introduction and examples of dynamical systems

2. Invariant measures and ergodic theory

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

4. Complete integrability, Liouville-Arnold theorem

5. Recurrence in topological dynamics, periodic orbits

6. Topological and metric entropies, Lyapounov exponents.

Grading: The grade will be based on a final project. The subject should be chosen around the middle of the semester. A ten page paper (or so) on a topic related to the course, expository or experimental, is expected.

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).