| January 19: (exceptional lecture, 2:00pm, room A2) |
Introduction to the course Symplectic linear algebra Symplectic manifolds and diffeomorphisms Darboux theorem |
|---|---|
| January 23: |
Symplectomorphisms Poincaré recurrence Hamiltonian diffeomorphisms Autonomous Hamiltonian flows The mathematical pendulum Contact manifolds |
| January 30: |
Reeb vector fields The Weinstein conjecture Gray stability and contact Darboux theorem Surfaces of section of 3-dimensional Reeb vector fields |
| February 6: |
Properties of the first return map of a global surface of section Introduction to Morse theory Deformation lemma Spectral values Lusternik-Schnirelmann theorem |
| February 20: |
Morse functions Morse lemma Morse inequalities |
| February 27: |
Genericity of Morse functions Morse theory on non-compact spaces Geodesic flows Existence of closed geodesics on closed Riemannian manifolds |
| March 6: | Theorem of the three simple closed geodesics |
| March 13: | The Arnold conjecture for Hamiltonian diffeomorphisms of tori |