Dynamical Systems

Catalog description

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. Prior exposure to topology (e.g., MATH 4530 ) will be helpful.