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

If time permits, we will also explore:

• Hamiltonian systems

• Bifurcation theory (e.g. Hopf bifurcations)

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 note (shared to students)

1. Introduction 

2. Linear system 

3. Existence and Uniqueness

4. Dynamic Systems

5. Invariant Manifolds

6. Phase Planes 

7. Chaotic Dynamics

8. Bifurcation Theory 

9. Hamiltonian Dynamics