Geodesic
Integrable billiard systems realize toric~foliations on lens spaces and the 3-torus
Sbornik. Mathematics, Tome 211 (2020) no. 2, pp. 201-225

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An integrable billiard system on a book, a complex of several billiard sheets glued together along the common spine, is considered. Each sheet is a planar domain bounded by arcs of confocal quadrics; it is known that a billiard in such a domain is integrable. In a number of interesting special cases of such billiards the Fomenko-Zieschang invariants of Liouville equivalence (marked molecules $W^*$) turn out to describe nontrivial toric foliations on lens spaces and on the 3-torus, which are isoenergy manifolds for these billiards. Bibliography: 18 titles.
Keywords: integrable system, billiard system
Mots-clés : Liouville equivalence, Fomenko-Zieschang invariant. 
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     title = {Integrable billiard systems realize toric~foliations on lens spaces and the 3-torus},
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V. V. Vedyushkina. Integrable billiard systems realize toric~foliations on lens spaces and the 3-torus. Sbornik. Mathematics, Tome 211 (2020) no. 2, pp. 201-225. http://geodesic.mathdoc.fr/item/SM_2020_211_2_a1/