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Sbornik: Mathematics, 2018, Volume 209, Issue 12, Pages 1690–1727
DOI: https://doi.org/10.1070/SM9039 (Mi sm9039) 		 
This article is cited in 38 scientific papers (total in 38 papers)

Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems

V. V. Vedyushkina, I. S. Kharcheva

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
English version PDF (852 kB) Citations (38) Russian version article
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DOI: https://doi.org/10.1070/SM9039
Abstract: We introduce a new class of billiards—billiard books, which are integrable Hamiltonian systems. It turns out that for any nondegenerate three-dimensional bifurcation (3-atom), a billiard book can be algorithmically constructed in which such a bifurcation appears. Consequently, any integrable Hamiltonian nondegenerate dynamical system with two degrees of freedom can be modelled in some neighbourhood of a critical leaf of the Liouville foliation in the iso-energy 3-manifold by a billiard.
Bibliography: 25 titles.
Keywords: integrable system, billiard, Liouville equivalence, Fomenko-Zieschang invariant.
Funding agency Grant number
Russian Science Foundation 17-11-01303
This research was supported by the Russian Science Foundation (project no. 17-11-01303).
Received: 20.11.2017
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: Primary 37J35; Secondary 37G10, 37J20, 70E40
Language: English
Original paper language: Russian
Citation: V. V. Vedyushkina, I. S. Kharcheva, “Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems”, Sb. Math., 209:12 (2018), 1690–1727
Citation in format AMSBIB
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    • This publication is cited in the following 38 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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