Graduate ODE (Math 716)

The topics we will cover include:

• Existence, uniqueness, and dependence on parameters

• Dynamical systems, flows and maps, orbits

• Linear equations and Floquet theory

• Stable and unstable invariant manifolds for equilibria and periodic orbits, center manifolds

• Planar systems: Poincaré–Bendixson theorem

• Bifurcation theory (e.g. Hopf bifurcations)

If time permits, we will also explore:

• Hamiltonian systems

While there is no official textbook, I will loosely follow Differential Dynamical Systems by James D. Meiss. 

References are Ordinary Differential Equations with Applications by Carmen Chicone 

Lecture notes and Problems with solutions

1. Introduction  note problems

2. Linear system note problems

3. Existence and Uniqueness note problems

4. Dynamic Systems note1 note2 problems

5. Invariant Manifolds  

6. Phase Planes 

7. Chaotic Dynamics  

8. Bifurcation Theory 

9. Hamiltonian Dynamics