Abstract:
In 2001, A. V. Borisov, I. S. Mamaev, and V. V. Sokolov discovered a new integrable case on the Lie algebra so(4)so(4). This is a Hamiltonian system with two degrees of freedom, where both the Hamiltonian and the additional integral are homogenous polynomials of degrees 2 and 4, respectively. In this paper, the topology of isoenergy surfaces for the integrable case under consideration on the Lie algebra so(4)so(4) and the critical points of the Hamiltonian under consideration for different values of parameters are described and the bifurcation values of the Hamiltonian are constructed. Also, a description of bifurcation complexes and typical forms of the bifurcation diagram of the system are presented.
Citation:
Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra so(4)so(4)”, Regul. Chaotic Dyn., 21:1 (2016), 1–17
\Bibitem{Akb16}
\by Rasoul Akbarzadeh
\paper Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 1
\pages 1--17
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\crossref{https://doi.org/10.1134/S1560354716010019}
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https://www.mathnet.ru/eng/rcd64
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This publication is cited in the following 6 articles:
V. D. Irtegov, T. N. Titorenko, “Ob odnom podkhode k kachestvennomu issledovaniyu nelineinykh dinamicheskikh sistem”, Sib. zhurn. vychisl. matem., 25:1 (2022), 59–75
V. D. Irtegov, T. N. Titorenko, “On an Approach to Qualitative Analysis of Nonlinear Dynamic Systems”, Numer. Analys. Appl., 15:1 (2022), 48
R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra $so(3,1)$”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736
A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525
P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20
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
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