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Sbornik: Mathematics, 2019, Volume 210, Issue 5, Pages 625–662
DOI: https://doi.org/10.1070/SM9120 (Mi sm9120) 		 
This article is cited in 15 scientific papers (total in 15 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
English version PDF (1387 kB) Citations (15)
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DOI: https://doi.org/10.1070/SM9120
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.
Received: 03.04.2018 and 21.12.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 5, Pages 3–40
DOI: https://doi.org/10.4213/sm9120
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
MSC: 37J35
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 15 articles:
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