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Sbornik: Mathematics, 2021, Volume 212, Issue 2, Pages 211–233
DOI: https://doi.org/10.1070/SM9418 (Mi sm9418) 		 
This article is cited in 10 scientific papers (total in 10 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
English version PDF (973 kB) Citations (10) Russian version article
References:
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DOI: https://doi.org/10.1070/SM9418
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.
Funding agency Grant number
Russian Science Foundation 17-11-01303
This work was supported by the Russian Science Foundation under grant no. 17-11-01303.
Received: 28.03.2020
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: 37C83, 37J35
Language: English
Original paper language: Russian
Citation: S. E. Pustovoitov, “Topological analysis of a billiard bounded by confocal quadrics in a potential field”, Sb. Math., 212:2 (2021), 211–233
Citation in format AMSBIB
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\paper Topological analysis of a~billiard bounded by confocal quadrics in a~potential field
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\vol 212
\issue 2
\pages 211--233
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:26
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