| January 8 |
Introduction to the course Symplectic linear algebra Symplectic manifolds, symplectomorphisms, and Hamiltonian diffeomorphisms Contact manifolds and Reeb flows |
|---|---|
| January 15: |
Symplectic geometry of tangent bundles Geodesic flows |
| January 22: |
The variational theory of geodesics Existence of a closed geodesic on any closed Riemannian manifold |
| January 29: |
Simple spectrum of a Riemannian 2-sphere Spectral characterization of Zoll 2-spheres Theorem of the three simple closed geodesics |
| February 5: |
The space of unparametrized simple loops on a closed surface Curve shortening flow |
| February 19: | Proof of the spectral characterization of Zoll 2-spheres |
| March 4: |
Surfaces of section of Reeb flows on closed 3-manifolds Poincaré recurrence theorem Hyperbolic dynamics: stable and unstable manifolds, heteroclinics, homoclinics |
| March 11: |
More hyperbolic dynamics: shadowing lemma, existence of periodic orbits Existence of global surfaces of section for geodesic flows of closed Riemannian surfaces |