GEOMETRY AND DYNAMICS OF GEODESIC FLOWS AND BILLIARDS
  Proposal for Special Topics Course for Fall 2006
               Maciej P. Wojtkowski

1. The tangent bundle, Levi-Civita, Weyl and metric connections.

2. The contangent bundle, symplectic structure and hamiltonian formalism.

3. Jacobi fields, torsion and curvature tensors.

4. Monotonicity and hyperbolicity in dynamical systems.

5. Design of hyperbolic billiards.

The course will be based on my papers and the book
of G.P. Paternain "Geodesic flows" (Birkhauser 1999).