MATH 6260

Dynamical Systems

Course Description

Course information provided by the Courses of Study 2024-2025.

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.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: MATH 4130-MATH 4140, or the equivalent. Exposure to topology (e.g., MATH 4530) will be helpful.

Comments Offered alternate years.

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