Nonlinear Dynamics and Chaos

Catalog description

This course is built around a concrete mechanical system, for example, the pendulum. Definition of dynamical systems, phase space flows and invariant subspaces. Local and global bifurcation theory: Saddle-node, transcritical, pitchfork, and Hopf bifurcations, sability of homoclinic orbits, center manifolds and normal forms. Chaos: fractal geometry and dimen-sion, Lyapunov exponents, routes to chaos (period doubling, qua-si-periodicity, intemittency), spatio-temporal chaos.