This article is cited in 14 papers

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

S. E. Pustovoitov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

Abstract: 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, Fomenko-Zieschang invariant, Liouville equivalence.

UDC: 517.938.5

MSC: 37C83, 37J35

Received: 28.03.2020

DOI: 10.4213/sm9418

 English version: Sbornik: Mathematics, 2021, 212:2, 211–233

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