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This article is cited in 6 scientific papers (total in 6 papers)
Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$
Rasoul Akbarzadeh Department of Fundamental Sciences, Azarbaijan Shahid Madani University, 35 Km Tabriz-Maragheh Road, Tabriz, Iran
Abstract:
In 2001, A. V. Borisov, I. S. Mamaev, and V. V. Sokolov discovered a new integrable case on the Lie algebra $so(4)$. 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 $so(4)$ 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.
Keywords:
topology, integrable Hamiltonian systems, isoenergy surfaces, critical set, bifurcation diagram, bifurcation complex, periodic trajectory.
Received: 17.09.2015 Accepted: 20.12.2015
Citation:
Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 21:1 (2016), 1–17
Linking options:
https://www.mathnet.ru/eng/rcd64 https://www.mathnet.ru/eng/rcd/v21/i1/p1
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