Periodic trajectories of ellipsoidal billiards in the 3-dimensional Minkowski space

Abstract

In this paper, we give detailed analysis and description of periodic trajectories of the billiard system within an ellipsoid in the 3-dimensional Minkowski space, taking into account all possibilities for the caustics. The conditions for periodicity are derived in algebro-geometric, analytic, and polynomial form.

arXiv comment14 pages, 2 figures