APMA 2190: Nonlinear Dynamical Systems: Theory and Applications (Fall 2010)
Class information
| Instructor | Björn Sandstede |
| Office | Room 325 in 182 George Street |
| Phone | 863-2815 |
| Email | bjorn_sandstede@brown.edu |
| Office Hours | Tuesdays 4-5, Thursdays 11-12, and by appointment |
| Class meetings | Tuesdays and Thursdays 2:30-3:50 in Wilson Hall 204 |
Project reports
A PDF file that contains all project reports is posted below:
Course material
This course provides a rigorous introduction to ordinary differential equations, studied from a dynamical-systems viewpoint. Motivated by examples from ecology, chemistry, mechanics, and physics, we will study the existence and uniqueness of solutions and the dynamical behavior near equilibria and periodic orbits.
- Existence and uniqueness, dependence on parameters
- Dynamical systems, flows and maps, orbits
- Linear equations and Floquet theory
- Stable and unstable invariant manifolds for equilibria and periodic orbits
- Planar systems: Poincare--Bendixson theorem
- Hamiltonian and gradient systems
- Center manifolds
- Normal forms
- Bifurcation theory for equilibria including Hopf bifurcations
The following topics will be covered in Spring:
- Melnikov method
- Horsehoes, and chaotic dynamics
- Averaging
- Geometric singular perturbation theory
- Lyapunov-Schmidt reduction
Literature
No textbook is required. Most of the material covered in the course can be found in
- C Chicone: Ordinary differential equations with applications, Springer
Other books that contain some or all of the material covered in the course are
- S-N Chow and J Hale: Methods of bifurcation theory, Springer
- H Amann: Ordinary differential equations, de Gryuter
- EA Coddington and N Levinson: Theory of ordinary differential equations, McGraw-Hill
- P Hartman: Ordinary differential equations, Wiley
