|
|
|
|
TOPIC # |
|
|
|
TOPICS |
|
|
|
|
|
|
|
|
1 |
|
|
|
One-Dimensional Systems and Elementary Bifurcations (about two weeks) |
|
|
|
|
|
|
|
|
2 |
|
|
|
Two-Dimensional Systems; Phase Plane Analysis, Limit Cycles, Poincaré-Bendixson Theory (about two weeks) |
|
|
|
|
|
|
|
|
3 |
|
|
|
Nonlinear Oscillators, Qualitative and Approximate Asymptotic Techniques, Hopf Bifurcations (about two weeks) |
|
|
|
|
|
|
|
|
4 |
|
|
|
Lorenz and Rossler Equations, Chaos, Strange Attractors and Fractals (about 2.5 weeks) |
|
|
|
|
|
|
|
|
5 |
|
|
|
Iterated Mappings, Period-Doubling, Chaos, Renormalization, Universality (about 1.5 weeks) |
|
|
|
|
|
|
|
|
6 |
|
|
|
Hamiltonian Systems; Complete Integrability and Ergodicity (about 1.5 weeks) |
|
|
|
|
|
|
|
|
7 |
|
|
|
Area Preserving Mappings, KAM theory (about 1.5 weeks) |
|
|
|
|
|
|
|
|
8 |
|
|
|
Other Topics (if time permits), such as: Infinite Dimensional Hamiltonian Systems, On-Off Dissipative Systems, etc. |
|
|
|
|
|