Topological analysis of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(4)\)

DOI10.1134/S1995080218090275zbMath1408.37095WikidataQ115247378 ScholiaQ115247378MaRDI QIDQ669546

Vladislav Kibkalo

Publication date: 15 March 2019

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fomenko-Zieschang invariantcritical point of centre-centre typeKovalevskaya integrable casemarked molecule

Mathematics Subject Classification ID

Related Items (11)

Topology of the isoenergy manifolds of the Kirchhoff rigid body case on \(e(3)\) ⋮ Liouville foliations of topological billiards with slipping ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ First Appelrot class of pseudo-Euclidean Kovalevskaya system ⋮ Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(3, 1)\) ⋮ Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras ⋮ Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(4) ⋮ Classification of the gluing matrices on the loop molecules of the points of center-center type ⋮ Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

Cites Work

• New approach to symmetries and singularities in integrable Hamiltonian systems
• Topological invariants of Liouville integrable Hamiltonian systems
• Bifurcation of common levels of first integrals of the Kovalevskaya problem
• The method of loop molecules and the topology of the Kovalevskaya top
• The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)
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