Dynamical Systems

Geometric theory of differential equations. Existence and uniqueness theorems; continuous dependence on initial conditions and parameters. Flows for autonomous and non-autonomous systems. Topological conjugacy and equivalence, Hartman-Grobman theorem. Stability theory. Non-autonomous linear systems and Floquet theory. Periodic solutions and Poincaré maps. Global methods, Liapunov theory and LaSalle invariance principle. Stable, unstable, and center manifolds. Structural stability and bifurcation theory. Symbolic dynamics and the shift map. Homoclinic phenomena.