Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia

N. S. Logacheva

Sbornik. Mathematics, Tome 203 (2012) no. 1, pp. 28-59

Résumé

The paper is devoted to a topological analysis of the Kovalevskaya-Yehia integrable case in rigid body dynamics. It is proved that the integral has the Bott property on isoenergy surfaces of the system; the topology of the Liouville foliation in a neighbourhood of degenerate 1-dimensional orbits and equilibria (points of rank 0) is also described. In particular, marked loop molecules are constructed for degenerate 1-dimensional orbits, and a representation in the form of an almost direct product is found for nondegenerate singularities of rank 0. Bibliography: 17 titles.

Détail

Keywords: nondegenerate equilibria, degenerate 1-dimensional orbits, loop molecules.
Mots-clés : moment map, Liouville foliation

Bibliographie

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