Applied Dynamical Systems

Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors; introduction to ergodic theory and the ergodic theorems.