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Mat. Sb., 2019, Volume 210, Number 5, Pages 3–40 (Mi msb9120)  

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

Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$

V. A. Kibkalo

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: This paper is concerned with the topology of the Liouville foliation in the analogue of the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$. The Fomenko-Zieschang invariants (that is, marked molecules) for this foliation are calculated on each nonsingular iso-energy surface. A detailed description of the resulting stratification of the three-dimensional space of parameters of the iso-energy surfaces is given.
Bibliography: 23 titles.

Keywords: integrable Hamiltonian systems, Kovalevskaya case, Liouville foliation, bifurcation diagram, topological invariants, Fomenko-Zieschang invariant.

Funding Agency Grant Number
Russian Science Foundation 17-11-01303
This work was supported by the Russian Science Foundation under grant no. 17-11-01303.


DOI: https://doi.org/10.4213/sm9120

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English version:
Sbornik: Mathematics, 2019, 210:5, 625–662

Bibliographic databases:

UDC: 517.938.5
MSC: 37J35
Received: 03.04.2018 and 21.12.2018

Citation: V. A. Kibkalo, “Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$”, Mat. Sb., 210:5 (2019), 3–40; Sb. Math., 210:5 (2019), 625–662

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107  mathnet  crossref  mathscinet  zmath  isi
    2. A. T. Fomenko, V. V. Vedyushkina, “Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: recent results”, Theor. Appl. Mech., 46:1 (2019), 47–63  mathnet  crossref
    3. Vedyushkina V.V., Fomenko A.T., “Reducing the Degree of Integrals of Hamiltonian Systems By Using Billiards”, Dokl. Math., 99:3 (2019), 266–269  crossref  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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