Quasi-BiHamiltonian Systems and Separability

Abstract

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.

10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997)

Cited by in corpus (35)

• Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
• Separation of variables for bi-Hamiltonian systems
• The quasi-bi-Hamiltonian formulation of the Lagrange top
• Degenerate Poisson pencils on curves: new separability theory
• On a Poisson reduction for Gel'fand--Zakharevich manifolds
• On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian
• Gaudin Models and Bending Flows: a Geometrical Point of View
• Haantjes Algebras of Classical Integrable Systems
• Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
• An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
• Generalized Lenard Chains, Separation of Variables and Superintegrability
• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator
• 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))
• Non-Noether symmetries in Hamiltonian Dynamical Systems
• Exact solutions for a class of integrable Henon-Heiles-type systems
• Families of quai-bi-Hamiltonian systems and separability
• Poisson Pencils, Integrability, and Separation of Variables
• A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability
• Towards a classification of natural bi-hamiltonian systems
• Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
• Haantjes Algebras of the Lagrange Top
• Bi-Hamiltonian aspects of the separability of the Neumann system
• Separable bi-Hamiltonian systems with quadratic in momenta first integrals
• Non-Hamiltonian systems separable by Hamilton-Jacobi method
• A Note on the Rotationally Symmetric SO(4) Euler Rigid Body
• Separability preserving Dirac reductions of Poisson pencils on Riemannian manifolds
• A class of Poisson-Nijenhuis structures on a tangent bundle
• Korteweg-de Vries hierarchy and related completely integrable systems: I. Algebro-geometrical approach
• Integrable systems whose spectral curve is the graph of a function
• A geometric approach to the separability of the Neumann-Rosochatius system
• Bi-hamiltonian Geometry and Separation of Variables for Gaudin Models: a case study
• Gel'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited
• Complex functions and geometric structures associated to the superintegrable Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion