Topological invariants of Liouville integrable Hamiltonian systems
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Publication:911118
DOI10.1007/BF01077420zbMath0697.58021MaRDI QIDQ911118
Publication date: 1988
Published in: Functional Analysis and its Applications (Search for Journal in Brave)
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items (30)
Structurally stable nondegenerate singularities of integrable systems ⋮ Realizability of singular levels of Morse functions as unions of geodesics ⋮ Height atoms whose symmetry groups act transitively on their vertex sets ⋮ Topological analysis corresponding to the Borisov-Mamaev-Sokolov integrable system on the Lie algebra \(\mathrm{so}(4)\) ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Integer lattices of the action variables for the generalized Lagrange case ⋮ Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities ⋮ One more proof of Vassiliev’s conjecture ⋮ New approach to symmetries and singularities in integrable Hamiltonian systems ⋮ Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat ⋮ Classification of singularities of the Liouville foliation of an integrable elliptical Billiard with a potential of fourth degree ⋮ Noncompact bifurcations of integrable dynamic systems ⋮ Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case ⋮ Topological invariants for elliptical billiards and geodesics on ellipsoids in the Minkowski space ⋮ Billiard Systems as the Models for the Rigid Body Dynamics ⋮ Parity in knot theory and graph-links ⋮ Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds ⋮ The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid ⋮ Phase topology of one system with separated variables and singularities of the symplectic structure ⋮ Topological analysis of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(4)\) ⋮ The topology of Liouville foliation for the Borisov-Mamaev-Sokolov integrable case on the Lie algebra \(so(4)\) ⋮ Fomenko-Zieschang invariants of integrable systems with symplectic singularities ⋮ Criteria for the height of an atom ⋮ The topology of isoenergetic surfaces for the Borisov-Mamaev-Sokolov integrable case on the Lie algebra \(so(3, 1)\) ⋮ Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems ⋮ Topological analysis of a billiard bounded by confocal quadrics in a potential field ⋮ Topological billiards, conservation laws and classification of trajectories ⋮ The number of connected components in the preimage of a regular value of the momentum mapping for the geodesic flow on ellipsoid
Cites Work
- Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations
- Liouville integrability of Hamiltonian systems on Lie algebras
- The topology of surfaces of constant energy and bifurcation diagrams for integrable cases of the dynamics of a rigid body on so(4)
- ROUND MORSE FUNCTIONS AND ISOENERGY SURFACES OF INTEGRABLE HAMILTONIAN SYSTEMS
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