The course is a self contained introduction to ordinary differential equations at the graduate level.
Topics selected from:
- Existence, uniqueness, and continuous dependence of solutions on parameters.
- Implicit Function Theorem in Banach spaces
- Linear theory of differential equations.
- Stability, Lyapunov functions, invariant manifolds, local hyperbolic theory.
- Periodic orbits, Poincaré maps
- Bifurcations of fixed points
- Hopf bifurcations
- Normal forms, averaging method. Applications to bifurcations.
- Homoclinic orbits, Melnikov method, chaotic solutions.
Offered in spring 2021: Course website for 2021