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

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.



Titolo: Generalized Lenard chains and multi-separability of the Smorodinsky-Winternitz system.
Autori: 
TONDO, GIORGIO SALVATORE
Data di pubblicazione: 2014
Rivista: 
JOURNAL OF PHYSICS. CONFERENCE SERIES  
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.
Handle: http://hdl.handle.net/11368/2737499
Appare nelle tipologie:4.1 Contributo in Atti Convegno (Proceeding)

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http://hdl.handle.net/11368/2737499
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