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

Abstract

We discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi-bi-Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton-Jacobi equation.

12 pages, no figures, LaTeX 2.09, to be published in Report on Mathematical Physics

References in corpus (2)

• Quasi-BiHamiltonian Systems and Separability
• On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

Cited by in corpus (7)

• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• The quasi-bi-Hamiltonian formulation of the Lagrange top
• Haantjes Algebras of Classical Integrable Systems
• An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
• Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems
• Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))
• Haantjes Algebras of the Lagrange Top