English

Periodic billiard trajectories in polyhedra

Dynamical Systems 2011-04-07 v1

Abstract

We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a periodic orbit of length four (generalization of Fagnano's orbit for triangles), moreover we can study completly the orbit of points along this coding.

Keywords

Cite

@article{arxiv.1104.1051,
  title  = {Periodic billiard trajectories in polyhedra},
  author = {Nicolas Bedaride},
  journal= {arXiv preprint arXiv:1104.1051},
  year   = {2011}
}

Comments

15 pages, 3 figures

R2 v1 2026-06-21T17:50:11.966Z