Topological analysis of a billiard bounded by confocal quadrics in a potential field

Topological analysis of a billiard bounded by confocal quadrics in a potential field

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 Ha...

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Veröffentlicht in:Sbornik. Mathematics 2021-02, Vol.212 (2), p.211-233
1. Verfasser: Pustovoitov, S. E.
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Potential fields
Topology
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description 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.
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subjects Potential fields
Topology
title Topological analysis of a billiard bounded by confocal quadrics in a potential field
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