Periodic billiard trajectories in polyhedra

Details Periodic billiard trajectories in polyhedra Periodic billiard trajectories in polyhedra

2011-04-06

arxiv.org/abs/1104.1051v1

Forum geometricorum Volume 8 (2008), pages 107-120

Mathematics

Dynamical Systems

15 pages, 3 figures

Scientific paper

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.

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