Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables

DOI10.1016/S0034-4877(99)80167-0zbMath0982.37068arXivsolv-int/9811008MaRDI QIDQ1573825

Giorgio Tondo, Carlo Morosi

Publication date: 9 August 2000

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9811008

zbMATH Keywords

Hamilton-Jacobi separabilitybi-Hamiltonian Pfaffian

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Hamilton-Jacobi equations in mechanics (70H20) Dynamical systems methods for problems in mechanics (70G60)

Related Items

An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families, Haantjes algebras of the Lagrange top, Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry, Algebraic properties of compatible Poisson brackets, Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy, Quantized W-algebra of sl(2, 1) and Quantum Parafermions of Uq(^sl(2)), Haantjes structures for the Jacobi-Calogero model and the Benenti systems, Haantjes algebras of classical integrable systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• The Kowalevski top: its \(r\)-matrix interpretation and bihamiltonian formulation
• Completely integrable bi-Hamiltonian systems
• Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy
• On the Euler equation: Bi-Hamiltonian structure and integrals in involution
• Bi-Hamiltonian separable chains on Riemannian manifolds.
• On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian.
• On the integrability of stationary and restricted flows of the KdV hierarchy
• Bi-Hamiltonian structure of an integrable Henon-Heiles system
• A simple model of the integrable Hamiltonian equation
• About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus
• Quasi-bi-Hamiltonian systems and separability
• Non-Pfaffian quasi-bi-Hamiltonian systems with two degrees of freedom
• On separability of bi-Hamiltonian chain with degenerated Poisson structures
• A class of integrable Hamiltonian systems whose solutions are (perhaps) all completely periodic
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Two degrees of freedom quasi-bi-Hamiltonian systems
• Euler-Poisson Equations on Lie Algebras and the N-Dimensional Heavy Rigid Body