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Sbornik: Mathematics, 2016, Volume 207, Issue 3, Pages 358–399
DOI: https://doi.org/10.1070/SM8558 (Mi sm8558) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution

E. O. Kantonistova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (955 kB) Citations (17)
References:
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DOI: https://doi.org/10.1070/SM8558
Abstract: A topological classification, up to Liouville (leafwise) equivalence of integrable Hamiltonian systems given by flows with a smooth potential on two-dimensional surfaces of revolution is presented. It is shown that the restrictions of such systems to three-dimensional isoenergy surfaces can be modelled by the geodesic flows (without potential) of certain surfaces of revolution. It is also shown that in many important cases the systems under consideration are equivalent to other well-known mechanical systems.
Bibliography: 29 titles.
Keywords: integrable Hamiltonian systems, surfaces of revolution, Fomenko-Zieschang invariant, lattices of action variables.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00170
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 16-01-00170).
Received: 17.06.2015 and 31.08.2015
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 3, Pages 47–92
DOI: https://doi.org/10.4213/sm8558
Bibliographic databases:
Document Type: Article
UDC: 514.7+514.8
MSC: 37J35, 70H06
Language: English
Original paper language: Russian
Citation: E. O. Kantonistova, “Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution”, Mat. Sb., 207:3 (2016), 47–92; Sb. Math., 207:3 (2016), 358–399
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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    References:51
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