On a Poisson reduction for Gel'fand--Zakharevich manifolds

Abstract

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the Separation of Variables problem.

Latex, 14 pages. Proceeding of the Conference "Multi-Hamiltonian Structures: Geometric and Algebraic Aspects". August 9-18, 2001 Bedlewo, Poland. To appear in ROMP

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• Gaudin Models and Bending Flows: a Geometrical Point of View
• Bi-Hamiltonian representation of Stäckel systems
• Poisson Pencils, Integrability, and Separation of Variables
• Haantjes Algebras of the Lagrange Top
• Separable bi-Hamiltonian systems with quadratic in momenta first integrals
• Geometric reduction of Hamiltonian systems
• Stackel systems: bi-Hamiltonian property and systematic construction
• Bi-presymplectic representation of Liouville integrable systems and related separability theory