Geodesic
Topological analysis of a~billiard bounded by confocal quadrics in a~potential field
Sbornik. Mathematics, Tome 212 (2021) no. 2, pp. 211-233

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Consider a billiard in a plane domain bounded by confocal ellipses and hyperbolae. A Hooke potential acts on a point mass. This dynamical systems turns out to be completely Liouville integrable. A topological analysis of the Liouville foliation of isoenergy manifolds at all possible levels of the Hamiltonian is performed and the complete Fomenko-Zieschang invariants (marked molecules) of these manifolds are constructed. Bibliography: 15 titles.
Keywords: Hooke potential, integrable system
Mots-clés : Fomenko-Zieschang invariant, Liouville equivalence. 
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     author = {S. E. Pustovoitov},
     title = {Topological analysis of a~billiard bounded by confocal quadrics in a~potential field},
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S. E. Pustovoitov. Topological analysis of a~billiard bounded by confocal quadrics in a~potential field. Sbornik. Mathematics, Tome 212 (2021) no. 2, pp. 211-233. http://geodesic.mathdoc.fr/item/SM_2021_212_2_a3/