MATH 6170: Dynamical Systems (Fall 2012)

Instructor: John Guckenheimer

This course is a rigorous introduction to dynamical systems theory. It will present the mathematical foundations for what has come to be known as “chaos theory.” Lectures will assume familiarity with undergraduate real analysis.

From the catalog: Topics include existence and uniqueness theorems for ODEs; Poincaré-Bendixon theorem and global properties of two dimensional flows; limit sets, nonwandering sets, chain recurrence, pseudo-orbits and structural stability; linearization at equilibrium points: stable manifold theorem and the Hartman-Grobman theorem; and generic properties: transversality theorem and the Kupka-Smale theorem. Examples include expanding maps and Anosov diffeomorphisms; hyperbolicity: the horseshoe and the Birkhoff-Smale theorem on transversal homoclinic orbits; rotation numbers; Herman’s theorem; and characterization of structurally stable systems.