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
Falqui, G., Pedroni, M. (2002). On a Poisson reduction for Gel'fand-Zakharevich manifolds. REPORTS ON MATHEMATICAL PHYSICS, 50(3), 395-407 [10.1016/S0034-4877(02)80068-4].
On a Poisson reduction for Gel'fand-Zakharevich manifolds
Falqui, G;
2002
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
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