Geodesic
The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)
Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 532-572

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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, bifurcation diagram, topological invariants.
Mots-clés : Liouville foliation 
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     author = {I. K. Kozlov},
     title = {The topology of the {Liouville} foliation for the {Kovalevskaya} integrable case on the {Lie} algebra so(4)},
     journal = {Sbornik. Mathematics},
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I. K. Kozlov. The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4). Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 532-572. http://geodesic.mathdoc.fr/item/SM_2014_205_4_a4/