Topological atlas of the Kowalevski-Sokolov top

DOI10.1134/S1560354716010032zbMath1398.70014MaRDI QIDQ283029

Pavel E. Ryabov, Mikhail P. Kharlamov, Alexander Yu. Savushkin

Publication date: 13 May 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

relative equilibriabifurcation diagramsintegrable Hamiltonian systemsisoenergy surfacescritical subsystemsrough topological invariants

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Motion of a rigid body with a fixed point (70E17)

Related Items

Topology of the isoenergy manifolds of the Kirchhoff rigid body case on \(e(3)\), 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, Topology of Liouville foliations of integrable billiards on table-complexes, Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

Cites Work

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• Topological analysis of an integrable system related to the rolling of a ball on a sphere
• Phase topology of one system with separated variables and singularities of the symplectic structure
• Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields
• On certain integrable motions of a rigid body acted upon by gravity and magnetic fields
• Bifurcation of common levels of first integrals of the Kovalevskaya problem
• New integrable cases in the dynamics of rigid bodies
• Bifurcation set and integral manifolds of the problem concerning the motion of a rigid body in a linear force field
• A new integrable case for the Kirchhoff equation
• Lax pairs for the deformed Kowalevski and Goryachev--Chaplygin tops
• Bifurcation analysis and the Conley index in mechanics
• Integrable Hamiltonian systems on Lie groups: Kowalewski type
• Bifurcation diagrams of the Kowalevski top in two constant fields
• Phase topology of one irreducible integrable problem in the dynamics of a rigid body
• Systems of Kowalevski type and discriminantly separable polynomials
• Extensions of the Appelrot classes for the generalized gyrostat in a double force field
• The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta functions via discriminantly separable polynomials
• Topology and mechanics. I
• Bifurcations of first integrals in the Sokolov case
• The electronic atlas of bifurcation diagrams of the Kowalevski–Yehia gyrostat
• Smale–Fomenko diagrams and rough topological invariants of the Kowalevski–Yehia case
• Kowalewski's top on the Lie algebras o(4), e(3), and o(3,1)
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
• Topology and stability of integrable systems
• Symmetry in systems with gyroscopic forces
• INTEGRABLE EULER EQUATIONS ON LIE ALGEBRAS ARISING IN PROBLEMS OF MATHEMATICAL PHYSICS
• Computation of the fine Fomenko-Zieschang invariant for the main integrable cases of rigid body motion
• Poisson maps and integrable deformations of the Kowalevski top
• The method of loop molecules and the topology of the Kovalevskaya top
• Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations
• Bifurcation diagrams on iso-energetic levels of the Kowalevski-Yehia gyrostat
• On an integrable deformation of the Kowalevski top
• The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)
• Kovalevskaya top and generalizations of integrable systems