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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 37 scientific papers (total in 37 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 (37)
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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
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 12, Pages 17–56
DOI: https://doi.org/10.4213/sm9039
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”, Mat. Sb., 209:12 (2018), 17–56; Sb. Math., 209:12 (2018), 1690–1727
Citation in format AMSBIB
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    • This publication is cited in the following 37 articles:
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