%0 Journal Article
%T Generalized Lenard Chains, Separation of Variables and Superintegrability
%A Piergiulio Tempesta
%A Giorgio Tondo
%J Physics
%D 2012
%I arXiv
%R 10.1103/PhysRevE.85.046602
%X We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.
%U http://arxiv.org/abs/1205.6937v1