PERIODIC BILLIARD TRAJECTORIES IN POLYHEDRA

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 (generaliza-tion of Fagnano’s orbit for triangles), moreover we can study completly the orbit of points along this coding. 1