Geodesic
A~topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
Sbornik. Mathematics, Tome 206 (2015) no. 10, pp. 1463-1507

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A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence. Bibliography: 18 titles.
Keywords: integrable system
Mots-clés : billiard, Liouville equivalence, Fomenko-Zieschang invariant. 
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     author = {V. V. Fokicheva},
     title = {A~topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics},
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V. V. Fokicheva. A~topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics. Sbornik. Mathematics, Tome 206 (2015) no. 10, pp. 1463-1507. http://geodesic.mathdoc.fr/item/SM_2015_206_10_a4/