Abstract:
This paper is concerned with the topology of the Liouville foliation in the analogue of the Kovalevskaya integrable case on the Lie algebra so(4)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.
Citation:
V. A. Kibkalo, “Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(4)so(4)”, Sb. Math., 210:5 (2019), 625–662
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\by V.~A.~Kibkalo
\paper Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$
\jour Sb. Math.
\yr 2019
\vol 210
\issue 5
\pages 625--662
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Linking options:
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This publication is cited in the following 17 articles:
G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
E. S. Agureeva, V. A. Kibkalo, “Topological analysis of axisymmetric Zhukovsky system for the case of the Lie algebra $e(2,1)$”, Moscow University Mathematics Bulletin, 79:5 (2024), 207–222
V. A. Kibkalo, D. A. Tuniyants, “Uporyadochennye billiardnye igry i topologicheskie svoistva billiardnykh knizhek”, Trudy Voronezhskoi zimnei matematicheskoi shkoly S. G. Kreina — 2024, SMFN, 70, no. 4, Rossiiskii universitet druzhby narodov, M., 2024, 610–625
V. A. Kibkalo, “Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat”, Moscow University Mathematics Bulletin, 78:1 (2023), 28–36
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
V. A. Kibkalo, “Pervyi klass Appelrota psevdoevklidovoi sistemy Kovalevskoi”, Chebyshevskii sb., 24:1 (2023), 69–88
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), 317–332
A. T. Fomenko, V. V. Vedyushkina, V. N. Zav'yalov, “Liouville foliations of topological billiards with slipping”, Russ. J. Math. Phys., 28:1 (2021), 37–55
V. V. Vedyushkina, A. T. Fomenko, “Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases”, Dokl. Math., 103:1 (2021), 1–4
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
Anatoly T. Fomenko, Vladislav A. Kibkalo, Understanding Complex Systems, Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, 2021, 3
V. A. Kibkalo, “Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:6 (2020), 263–267
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
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
V. V. Vedyushkina, A. T. Fomenko, “Reducing the degree of integrals of hamiltonian systems by using billiards”, Dokl. Math., 99:3 (2019), 266–269
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