Abstract:
Several new integrable cases for Euler's equations on some six-dimensional Lie algebras were found by Sokolov in 2004. In this paper we study topological properties of one of these integrable cases on
the Lie algebra so(4). In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, the classification of
isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
Bibliography: 9 titles.
Citation:
G. Haghighatdoost, A. A. Oshemkov, “The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4)”, Sb. Math., 200:6 (2009), 899–921
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\by G.~Haghighatdoost, A.~A.~Oshemkov
\paper The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4)
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\yr 2009
\vol 200
\issue 6
\pages 899--921
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This publication is cited in the following 11 articles:
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, “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
Anatoly T. Fomenko, Kirill I. Solodskih, Understanding Complex Systems, Modern Mathematics and Mechanics, 2019, 13
Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592
Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra so(4)”, Regul. Chaotic Dyn., 20:3 (2015), 317–344
I. K. Kozlov, “The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)”, Sb. Math., 205:4 (2014), 532–572
D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra so(3,1)”, Sb. Math., 205:8 (2014), 1107–1132
D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra e(3)”, Sb. Math., 202:5 (2011), 749–781
Novikov D.V., “The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra so(3,1)”, Moscow Univ. Math. Bull., 66:4 (2011), 181–184
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