The course is a self contained introduction to ordinary differential equations at the graduate level.
- Existence, uniqueness, and continuous dependence of solutions on parameters.
- Linear theory of differential equations.
- Stability, Lyapunov functions, invariant manifolds, local hyperbolic theory.
- Periodic orbits, Poincare-Bendixon theory.
- Normal forms, averaging method. Applications to bifurcations.
- Homoclinic orbits, Melnikov method, chaotic solutions.
Not offered in 2016-2017