Generalized Lenard chains and multi-separability of the Smorodinsky_Winternitz system

Physics and Mathematics of Nonlinear Phenomena 2013

Tondo, Giorgio^1

Dipartimento di Matematica e Geoscienze, Università Degli Studi di Trieste, Piaz.le Europa 1, I-34127 Trieste, Italy^1

关键词: Separation of variables;    Symplectic;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012042/pdf
DOI  :  10.1088/1742-6596/482/1/012042

来源: IOP

【 摘 要 】

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.