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This article is cited in 12 scientific papers (total in 12 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
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.
Received: 02.11.2018 and 23.04.2019
Citation:
V. V. Vedyushkina, “Integrable billiard systems realize toric foliations on lens spaces and the 3-torus”, Sb. Math., 211:2 (2020), 201–225
Linking options:
https://www.mathnet.ru/eng/sm9189https://doi.org/10.1070/SM9189 https://www.mathnet.ru/eng/sm/v211/i2/p46
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Abstract page: | 489 | Russian version PDF: | 81 | English version PDF: | 38 | References: | 49 | First page: | 18 |
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