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

@inproceedings{Tondo2014GeneralizedLC,
  title={Generalized Lenard chains and multi-separability of the Smorodinsky–Winternitz system},
  author={Giorgio Tondo},
  year={2014}
}
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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