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This article is cited in 9 scientific papers (total in 9 papers)
Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$
D. V. Novikov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The Sokolov integrable case on $\mathrm{e}(3)^{\star}$ is investigated. This is a Hamiltonian system with $2$ degrees of freedom in which the Hamiltonian and the additional integral are homogeneous polynomials having degree $2$ and $4$, respectively. This system is of interest because connected joint level surfaces of the Hamiltonian and the additional integral are noncompact. The critical points of the moment map and their
indices are found, the bifurcation diagram is constructed and the Liouville foliation of the system is described. The Hamiltonian vector fields corresponding to the Hamiltonian and the additional integral are proved to be complete.
Bibliography: 22 titles.
Keywords:
integrable Hamiltonian systems, completeness of vector fields, bifurcation diagram, moment map, noncompact singularities.
Received: 23.11.2010
Citation:
D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$”, Mat. Sb., 202:5 (2011), 127–160; Sb. Math., 202:5 (2011), 749–781
Linking options:
https://www.mathnet.ru/eng/sm7823https://doi.org/10.1070/SM2011v202n05ABEH004165 https://www.mathnet.ru/eng/sm/v202/i5/p127
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Abstract page: | 551 | Russian version PDF: | 202 | English version PDF: | 4 | References: | 55 | First page: | 39 |
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