Geodesic
Topological type of isoenergy surfaces of billiard books
Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1660-1674

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The homeomorphism class of the isoenergy surface of a billiard book, of low complexity and not necessarily integrable, is determined using methods of low-dimensional topology. In particular, a series of billiard books is constructed that realize isoenergy 3-surfaces homeomorphic to the connected sum of a number of lens spaces and direct products $S^1\times S^2$. The Fomenko-Zieschang invariants, which classify Liouville foliations on isoenergy surfaces up to fibrewise homeomorphisms – that is, up to Liouville equivalence of the corresponding integrable Hamiltonian systems – are calculated for several integrable billiards of this type. Bibliography: 14 titles.
Keywords: integrable system
Mots-clés : billiard book, Liouville equivalence, Fomenko-Zieschang invariant. 
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     author = {V. V. Vedyushkina},
     title = {Topological type of isoenergy surfaces of billiard books},
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V. V. Vedyushkina. Topological type of isoenergy surfaces of billiard books. Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1660-1674. http://geodesic.mathdoc.fr/item/SM_2021_212_12_a0/