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Sbornik: Mathematics, 2021, Volume 212, Issue 8, Pages 1122–1179
DOI: https://doi.org/10.1070/SM9468
(Mi sm9468)
 

This article is cited in 12 scientific papers (total in 12 papers)

Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems

V. V. Vedyushkina, I. S. Kharcheva

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
References:
Abstract: We consider a generalization of a mathematical billiard bounded by arcs of confocal quadrics, known as billiard books. Billiard books define a large class of integrable Hamiltonian systems. In this connection the question arises of the possibility of realizing integrable Hamiltonian systems with two degrees of freedom by billiard books. The authors have proved previously that for any nondegenerate three-dimensional bifurcation ($3$-atom) a billiard book in which such a bifurcation appears can be constructed algorithmically. Based on the preceding result, we give a proof of the fact that given any base of a Liouville foliation (rough molecule), a billiard book can be constructed algorithmically such that the base of the Liouville foliation of this system is isomorphic to the one given initially.
Bibliography: 15 titles.
Keywords: mathematical billiard, Hamiltonian system, Liouville equivalence, Fomenko-Zieschang invariant.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00775-а
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS 19-8-2-5-1
The research of I. S. Kharcheva was supported by the Russian Foundation for Basic Research (grant no. 19-01-00775-a) and by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” (grant no. 19-8-2-5-1).
Received: 24.06.2020
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: Primary 37J35; Secondary 37G10, 37J20
Language: English
Original paper language: Russian
Citation: V. V. Vedyushkina, I. S. Kharcheva, “Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems”, Sb. Math., 212:8 (2021), 1122–1179
Citation in format AMSBIB
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\by V.~V.~Vedyushkina, I.~S.~Kharcheva
\paper Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems
\jour Sb. Math.
\yr 2021
\vol 212
\issue 8
\pages 1122--1179
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\crossref{https://doi.org/10.1070/SM9468}
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  • https://doi.org/10.1070/SM9468
  • https://www.mathnet.ru/eng/sm/v212/i8/p89
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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