V. A. Kibkalo, “The topology of the analog of Kovalevskaya integrability case on the Lie algebra $\mathrm{so}(4)$ under zero area integral”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 3, 46–50; Moscow University Mathematics Bulletin, 71:3 (2016), 119

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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika

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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 3, Pages 46–50 (Mi vmumm153)

This article is cited in 9 scientific papers (total in 9 papers)

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The topology of the analog of Kovalevskaya integrability case on the Lie algebra $\mathrm{so}(4)$ under zero area integral

V. A. Kibkalo

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (603 kB) Citations (9)

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Abstract: We study the topology of the space of the solutions closure for the integrable system on the Lie algebra $\mathrm{so}(4)$ that is an analogue of the Kovalevskaya case. For this purpose Fomenko–Zieschang invariants are calculated in the case of zero area integral, which classify isoenergetic $3$-surfaces and corresponding Liouville foliation on them.

Key words: integrable Hamiltonian system, Fomenko–Zieschang invariants, isoenergetic surface.

Received: 27.05.2015

English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 3, Pages 119–123
DOI: https://doi.org/10.3103/S0027132216030074

Bibliographic databases:

Document Type: Article

UDC: 517.938.5

Language: Russian

Citation: V. A. Kibkalo, “The topology of the analog of Kovalevskaya integrability case on the Lie algebra $\mathrm{so}(4)$ under zero area integral”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 3, 46–50; Moscow University Mathematics Bulletin, 71:3 (2016), 119–123

Citation in format AMSBIB

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Linking options:

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https://www.mathnet.ru/eng/vmumm/y2016/i3/p46

This publication is cited in the following 9 articles:

G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
G. V. Belozerov, “Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space”, Sb. Math., 213:2 (2022), 129–160
A. T. Fomenko, V. V. Vedyushkina, “Evolutionary force billiards”, Izv. Math., 86:5 (2022), 943–979
A. T. Fomenko, V. V. Vedyushkina, “Billiards with Changing Geometry and Their Connection with the Implementation of the Zhukovsky and Kovalevskaya Cases”, Russ. J. Math. Phys., 28:3 (2021), 317
A. T. Fomenko, V. V. Vedyushkina, V. N. Zav'yalov, “Liouville Foliations of Topological Billiards with Slipping”, Russ. J. Math. Phys., 28:1 (2021), 37
V. A. Kibkalo, A. T. Fomenko, I. S. Kharcheva, “Realizing integrable Hamiltonian systems by means of billiard books”, Trans. Moscow Math. Soc., 82 (2021), 37–64
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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