Periodic trajectories in 3-dimensional convex billiards

Michael Farber; Serge Tabachnikov

Periodic trajectories in 3-dimensional convex billiards

Differential Geometry 2007-05-23 v1 Algebraic Topology

Authors: Michael Farber , Serge Tabachnikov

Abstract

We give lower bound on the number of periodic billiard trajectories inside a generic smooth strictly convex closed surface in 3-space: for odd n, there are at least 2(n-1) such trajectories. We apply a topological approach based on the calculation of cohomology of certain configuration spaces.

Keywords

billiards periodic orbits in hamiltonian systems manifolds

Cite

@article{arxiv.math/0106049,
  title  = {Periodic trajectories in 3-dimensional convex billiards},
  author = {Michael Farber and Serge Tabachnikov},
  journal= {arXiv preprint arXiv:math/0106049},
  year   = {2007}
}