Topological features of the Sokolov integrable case on the Lie algebra so(3,1)

Journal Article · Sun Aug 31 00:00:00 EDT 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014v205n08ABEH004412· OSTI ID:22364911

Novikov, D V ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

The integrable Sokolov case on so(3,1){sup ⋆} is investigated. This is a Hamiltonian system with two degrees of freedom, in which the Hamiltonian and the additional integral are homogeneous polynomials of degrees 2 and 4, respectively. It is an interesting feature of this system that connected components of common level surfaces of the Hamiltonian and the additional integral turn out to be noncompact. The critical points of the moment map and their indices are found, the bifurcation diagram is constructed, and the topology of noncompact level surfaces is determined, that is, the closures of solutions of the Sokolov system on so(3,1) are described. Bibliography: 24 titles.

• OSTI ID: 22364911
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 8; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BIFURCATION
DEGREES OF FREEDOM
DIAGRAMS
HAMILTONIANS
INTEGRAL CALCULUS
INTEGRALS
LIE GROUPS
MATHEMATICAL SOLUTIONS
POLYNOMIALS
SO GROUPS
TOPOLOGY