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Sbornik: Mathematics, 2020, Volume 211, Issue 8, Pages 1127–1158
DOI: https://doi.org/10.1070/SM9349 (Mi sm9349) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds

S. S. Nikolaenkoab

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
English version PDF (854 kB) Citations (12)
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DOI: https://doi.org/10.1070/SM9349
Abstract: We construct a complete topological invariant of foliations of finite type defined by smooth functions on two-dimensional noncompact orientable manifolds. In particular, we describe a complete topological classification of noncompact bifurcations of such foliations. We establish a natural one-to-one correspondence between the set of all such bifurcations and the set of oriented coloured graphs of a special form. As a consequence, we obtain the Liouville and trajectory classifications of Hamiltonian systems of finite type on noncompact two-dimensional manifolds.
Bibliography: 25 titles.
Keywords: Hamiltonian system, topological classification, trajectory equivalence, noncompact atom, $f$-graph.
Funding agency Grant number
Russian Science Foundation 17-11-01303
This research was supported by a grant from the Russian Science Foundation (project no. 17-11-01303).
Received: 13.11.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 8, Pages 68–101
DOI: https://doi.org/10.4213/sm9349
Bibliographic databases:
Document Type: Article
UDC: 514.853+517.938.5
MSC: Primary 37J35; Secondary 37G10, 58K45, 70H06
Language: English
Original paper language: Russian
Citation: S. S. Nikolaenko, “Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds”, Mat. Sb., 211:8 (2020), 68–101; Sb. Math., 211:8 (2020), 1127–1158
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:26
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