Course MAT582

Dynamical Systems

This course will concentrate on chaos in dynamical systems.  We will discuss Anosov (globally hyperbolic) diffeomorphisms and flows.  I intend to prove their topological stability and then discuss their stable and unstable foliations.  Anosov flows and diffeomorphisms are purely chaotic dynamical systems.  Ergodic theory provides a means to study chaos, and I intend to discuss the beginning of this study as it pertains to Anosov systems—Markov partitions and Gibbs measures.  Time permitting, I will discuss a bit about chaos in systems where random and stable motions exist side-by-side.

Description of Classes

Homework/Grading:  Problem sets (60%); Take-home midterm (30%); Paper in lieu of midterm (10%);

Placement and Prerequisites

For advanced level undergraduate and graduate students.