Description: Prereq- uisite(s): MATH 146B; MATH 151C; MATH 205C or MATH 232A; or consent of instructor. Explores diffeomorphisms and flows, Poincarâ maps, and Hamiltonian flows. Includes hyperbolicity, homoclinic points, center manifold theorem, structural stability, and Hopf bifurcations. Explores the Poincarâ-Birkhoff theorem, basin of attraction and strange attractors, and Lyapunov exponents and entropy. Introduces chaotic dynamical systems, KAM theory, and complex dynamics.