Billiards bounded by arcs of confocal quadrics on the Minkowski plane

Abstract

Billiards are considered in compact domains on a Minkowski plane whose boundary consists of arcs of confocal quadrics with angles at corner points . A classification is obtained for these billiards, called simple billiards. The first integrals and trajectories of the motion of a ball in simple billiards are described. The Fomenko-Zieschang invariants are calculated for every simple billiard, and a theorem is proved which shows that only three different Liouville foliations of simple billiards exist on the Minkowski plane. Bibliography: 23 titles.