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Mat. Sb., 2020, Volume 211, Number 2, Pages 46–73 (Mi msb9189)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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.


DOI: https://doi.org/10.4213/sm9189

Full text: PDF file (1251 kB)
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English version:
Sbornik: Mathematics, 2020, 211:2, 201–225

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37D50, 37J35; Secondary 37D40, 37J20, 70E40
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”, Mat. Sb., 211:2 (2020), 46–73; Sb. Math., 211:2 (2020), 201–225

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Vedyushkina, “Lokalnoe modelirovanie bilyardami sloenii Liuvillya: realizatsiya rebernykh invariantov”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 2, 28–32  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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