Periodic billiard trajectories in polyhedra

Nicolas Bedaride (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Domaines: Systèmes dynamiques [math.DS]

Nicolas Bedaride. Periodic billiard trajectories in polyhedra. Forum Geometricorum: A Journal on Classical Euclidean Geometry, 2008, 8, pp.107-120. ⟨hal-00920896⟩