MATH 628: Second Semester Dynamical Systems (Spring 2004)

Instructor: John Smillie

Meeting Time & Room

This course is designed to be a natural successor to MATH 617. In this course we will cover a chapter in the classical theory of dynamical systems, we will give an introduction to complex dynamics and we will explore examples and applications of the classical theory to some topics in complex dynamics and elsewhere.

Classical theory:

Hyperbolic dynamical systems
Shadowing
Topological semi-conjugacies and structural stability
Markov partitions and symbolic dynamics
Finitely presented dynamical systems

Complex dynamics:

Introduction to complex dynamics
Natural metrics in 1 complex dimension
Natural cone fields in 2 complex dimensions

Examples and applications:

Expanding maps of manifolds
Anosov diffeomorphisms
Julia sets, external rays and Hubbard trees
Solenoids and horseshoes in 2 complex dimensions

Students will be asked to give presentations on related topics or to explore some of the above topics in greater depth.

Last modified: October 23, 2003