We show that the notion of generalized Lenard chains allows to formulate in a natural way the theory of multi-separable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function and by a Nijenhuis tensor defined on a symplectic manifold guarantees the separation of variables. As an application, we construct such a chain for the case I of the classical Smorodinsky-Winternitz model.

Generalized Lenard chains and multi-separability of the Smorodinsky-Winternitz system.

TONDO, GIORGIO SALVATORE
2014

Abstract

We show that the notion of generalized Lenard chains allows to formulate in a natural way the theory of multi-separable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function and by a Nijenhuis tensor defined on a symplectic manifold guarantees the separation of variables. As an application, we construct such a chain for the case I of the classical Smorodinsky-Winternitz model.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2737499
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