CDS 140a -- Fall 2008
Introduction to Dynamical Systems
9 units (3-0-6); first term. Prerequisite: ACM 95 or equivalent
Basic theory of dynamical systems in Euclidean space, including equilibria, stability, Lyapunov functions, periodic solutions, Poincaré–Bendixon theory, Poincaré maps. The Euler–Lagrange equations, mechanical systems, dissipation, energy as a Lyapunov function, and simple conservation laws. Introduction to basic bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging, Melnikov's method, and the Smale horseshoe.