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Sbornik: Mathematics, 2015, Volume 206, Issue 10, Pages 1463–1507
DOI: https://doi.org/10.1070/SM2015v206n10ABEH004502 (Mi sm8506) 		 
This article is cited in 57 scientific papers (total in 57 papers)

A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics

V. V. Fokicheva

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (946 kB) Citations (57)
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DOI: https://doi.org/10.1070/SM2015v206n10ABEH004502
Abstract: A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence.
Bibliography: 18 titles.
Keywords: integrable system, billiard, Liouville equivalence, Fomenko-Zieschang invariant.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00081-a
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 13-01-00081-a).
Received: 12.03.2015 and 03.07.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 10, Pages 127–176
DOI: https://doi.org/10.4213/sm8506
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: Primary 37D50, 37J35; Secondary 70E40
Language: English
Original paper language: Russian
Citation: V. V. Fokicheva, “A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics”, Mat. Sb., 206:10 (2015), 127–176; Sb. Math., 206:10 (2015), 1463–1507
Citation in format AMSBIB
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    • This publication is cited in the following 57 articles:
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    English version PDF:9
    References:47
    First page:39
     
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