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Sbornik: Mathematics, 2020, Volume 211, Issue 2, Pages 201–225
DOI: https://doi.org/10.1070/SM9189 (Mi sm9189) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Integrable billiard systems realize toric foliations on lens spaces and the 3-torus

V. V. Vedyushkina

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (1083 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM9189
Abstract: An integrable billiard system on a book, a complex of several billiard sheets glued together along the common spine, is considered. Each sheet is a planar domain bounded by arcs of confocal quadrics; it is known that a billiard in such a domain is integrable. In a number of interesting special cases of such billiards the Fomenko-Zieschang invariants of Liouville equivalence (marked molecules $W^*$) turn out to describe nontrivial toric foliations on lens spaces and on the 3-torus, which are isoenergy manifolds for these billiards.
Bibliography: 18 titles.
Keywords: integrable system, billiard system, Liouville equivalence, Fomenko-Zieschang invariant.
Funding agency Grant number
Russian Science Foundation 17-11-01303
This research was supported by the Russian Science Foundation under grant no. 17-11-01303.
Received: 02.11.2018 and 23.04.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 2, Pages 46–73
DOI: https://doi.org/10.4213/sm9189
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: Primary 37D50, 37J35; Secondary 37D40, 37J20, 70E40
Language: English
Original paper language: Russian
Citation: V. V. Vedyushkina, “Integrable billiard systems realize toric foliations on lens spaces and the 3-torus”, Mat. Sb., 211:2 (2020), 46–73; Sb. Math., 211:2 (2020), 201–225
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
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