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Mat. Sb., 2008, Volume 199, Number 3, Pages 95–132 (Mi msb3914)  

This article is cited in 3 scientific papers (total in 3 papers)

Topology of the Liouville foliation on a 2-sphere in the Dullin-Matveev integrable case

A. Yu. Moskvin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper is concerned with the study of the topology of the Liouville foliations of the Dullin-Matveev integrable case. The critical point set of the Hamiltonian is found, the types of isoenergy surfaces are calculated, the non-degeneracy conditions are verified, the types of non-degenerate points of the Poisson action are determined, the moment map is investigated and the bifurcation diagram is constructed. A test for the Bott property is verified by numerical simulation. The indices of critical circles, the bifurcation types and the rough molecules are found. The rough Liouville classification of this integrable case is virtually accomplished as a result.
Bibliography: 24 titles.

DOI: https://doi.org/10.4213/sm3914

Full text: PDF file (703 kB)
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English version:
Sbornik: Mathematics, 2008, 199:3, 411–448

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37J35; Secondary 70H06
Received: 19.06.2007

Citation: A. Yu. Moskvin, “Topology of the Liouville foliation on a 2-sphere in the Dullin-Matveev integrable case”, Mat. Sb., 199:3 (2008), 95–132; Sb. Math., 199:3 (2008), 411–448

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. P. Kharlamov, P. E. Ryabov, “Diagrammy Smeila–Fomenko i grubye invarianty sluchaya Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 40–59  mathnet
    2. Fomenko A.T., Konyaev A.Yu., “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topology Appl., 159:7 (2012), 1964–1975  crossref  mathscinet  zmath  isi  elib  scopus
    3. Fomenko A.T. Vedyushkina V.V., “Singularities of Integrable Liouville Systems, Reduction of Integrals to Lower Degree and Topological Billiards: Recent Results”, Theor. Appl. Mech., 46:1 (2019), 47–63  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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