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Sbornik: Mathematics, 2018, Volume 209, Issue 5, Pages 739–758
DOI: https://doi.org/10.1070/SM8946 (Mi sm8946) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Graph-manifolds and integrable Hamiltonian systems

K. I. Solodskikh

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (565 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM8946
Abstract: We study the topology of the three-dimensional constant-energy manifolds of integrable Hamiltonian systems realizable in the form of a special class of so-called ‘molecules’. Namely, for this class of manifolds the Reidemeister torsion is calculated in terms of the Fomenko-Zieschang invariants. A connection between the torsion of a constant-energy manifold and stable periodic trajectories is found.
Bibliography: 17 titles.
Keywords: Reidemeister torsion, Waldhausen graph-manifold, Fomenko-Zieschang invariants, marked molecules, Hamiltonian systems.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
This research was conducted within the framework of the Programme of the President of the Russian Federation for state support of leading scientific schools of the Russian Federation (grant no. НШ-6399.2018.1).
Received: 23.03.2017 and 19.02.2018
Bibliographic databases:
Document Type: Article
UDC: 514.853
MSC: Primary 37J35; Secondary 37C15
Language: English
Original paper language: Russian
Citation: K. I. Solodskikh, “Graph-manifolds and integrable Hamiltonian systems”, Sb. Math., 209:5 (2018), 739–758
Citation in format AMSBIB
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\paper Graph-manifolds and integrable Hamiltonian systems
\jour Sb. Math.
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\vol 209
\issue 5
\pages 739--758
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:479
    Russian version PDF:73
    English version PDF:21
    References:46
    First page:14
     
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