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

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

2002-04-19

arxiv.org/abs/nlin/0204050v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex, 14 pages. Proceeding of the Conference "Multi-Hamiltonian Structures: Geometric and Algebraic Aspects". August 9-18, 20

Scientific paper

10.1016/S0034-4877(02)80068-4

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.

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