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.
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