Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$

V. A. Kibkalo

Sbornik. Mathematics, Tome 210 (2019) no. 5, pp. 625-662

Résumé

This paper is concerned with the topology of the Liouville foliation in the analogue of the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$. The Fomenko-Zieschang invariants (that is, marked molecules) for this foliation are calculated on each nonsingular iso-energy surface. A detailed description of the resulting stratification of the three-dimensional space of parameters of the iso-energy surfaces is given. Bibliography: 23 titles.

Détail

Keywords: integrable Hamiltonian systems, Kovalevskaya case, bifurcation diagram, topological invariants
Mots-clés : Liouville foliation, Fomenko-Zieschang invariant.

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