Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space

Abstract

We consider geodesic billiards on quadrics in . We consider the motion of a point mass inside a billiard table, that is, inside a domain lying on a quadric bounded by finitely many quadrics confocal with the given one and having angles at corner points of the boundary equal to . According to the well-known Jacobi-Chasles theorem this problem turns out to be integrable. We introduce an equivalence relation on the set of billiard tables and prove a theorem on their classification. We present a complete classification of geodesic billiards on quadrics in up to Liouville equivalence. Bibliography: 19 titles.