Theory of tensor invariants of integrable Hamiltonian systems. I: Incompatible Poisson structures

DOI10.1007/BF02099623zbMath0861.58021OpenAlexW2041365405MaRDI QIDQ1924100

Oleg I. Bogoyavlenskij

Publication date: 12 May 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099623

zbMATH Keywords

Poisson structureintegrable Hamiltonian systemcomplete integrabilitydynamical compatibility

Mathematics Subject Classification ID

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) Celestial mechanics (70F15)

Related Items

On integrable systems outside Nijenhuis and Haantjes geometry, Nekhoroshev and KAM stabilities in generalized Hamiltonian systems, Hamiltonian Dynamics of a spaceship in Alcubierre and G\"odel metrics: Recursion operators and underlying master symmetries, Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space, Algebraic identity for the Schouten tensor and bi-Hamiltonian systems, Magri–Morosi–Gel’fand–Dorfman’s bi-Hamiltonian constructions in the action-angle variables, Poisson quasi-Nijenhuis manifolds and the Toda system, Global structure and geodesics for Koenigs superintegrable systems, Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures, The action-angle coordinates revisited: bi-Hamiltonian systems, Noncommutative integrability and recursion operators, Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds, Compatibility of symplectic structures adapted to noncommutatively integrable systems, Schouten tensor and bi-Hamiltonian systems of hydrodynamic type

Cites Work

• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Hamiltonian operators and algebraic structures related to them
• The Schouten bracket and Hamiltonian operators
• Reduction of symplectic manifolds with symmetry
• Les variétés de Poisson et leurs algèbres de Lie associees
• Geometry of bi-Hamiltonian systems
• Completely integrable bi-Hamiltonian systems
• Sur l'analysis situs des variétés à \(n\) dimensions
• The Poincaré-Lyapunov-Liouville-Arnol'd theorem
• Convergent series expansions for quasi-periodic motions
• Differential forms in manifolds with boundary
• Harmonic tensors on Riemannian manifolds with boundary
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems
• Semidirect Products and Reduction in Mechanics
• Application of hereditary symmetries to nonlinear evolution equations
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• A simple model of the integrable Hamiltonian equation
• About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus
• Recursion operators: Meaning and existence for completely integrable systems
• Invariant incompatible Poisson structures
• A Definition of the Exterior Derivative in Terms of Lie Derivatives
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item