|
This article is cited in 14 scientific papers (total in 14 papers)
The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)
I. K. Kozlov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra so(4), which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the
momentum mapping are constructed, the types of critical points of rank 0 are determined, the bifurcations of Liouville tori are described, and the loop molecules are computed for all singular points of the bifurcation diagrams. It follows from the obtained results that some topological properties of the classical Kovalevskaya case can be obtained from the corresponding properties of the considered integrable case on the Lie algebra
so(4) by taking a natural limit.
Bibliography: 21 titles.
Keywords:
integrable Hamiltonian systems, Kovalevskaya case, Liouville foliation, bifurcation diagram, topological invariants.
Received: 13.11.2013
Citation:
I. K. Kozlov, “The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)”, Mat. Sb., 205:4 (2014), 79–120; Sb. Math., 205:4 (2014), 532–572
Linking options:
https://www.mathnet.ru/eng/sm8299https://doi.org/10.1070/SM2014v205n04ABEH004387 https://www.mathnet.ru/eng/sm/v205/i4/p79
|
Statistics & downloads: |
Abstract page: | 484 | Russian version PDF: | 129 | English version PDF: | 9 | References: | 68 | First page: | 36 |
|