Billiards bounded by arcs of confocal quadrics on the Minkowski plane

E. E. Karginova

Sbornik. Mathematics, Tome 211 (2020) no. 1, pp. 1-28

Résumé

Billiards are considered in compact domains on a Minkowski plane whose boundary consists of arcs of confocal quadrics with angles at corner points $\le\pi/2$. 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.

Détail

Keywords: integrable system, Minkowski plane
Mots-clés : billiard, Liouville equivalence, Fomenko-Zieschang invariant.

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