Math 716: Ordinary Differential Equations

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