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• W2000700975 abstract "We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multiseparable 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 $ensuremath{omega}N$ 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." @default.
• W2000700975 created "2016-06-24" @default.
• W2000700975 creator A5038563250 @default.
• W2000700975 creator A5080845237 @default.
• W2000700975 date "2012-04-03" @default.
• W2000700975 modified "2023-10-10" @default.
• W2000700975 title "Generalized Lenard chains, separation of variables, and superintegrability" @default.
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• W2000700975 doi "https://doi.org/10.1103/physreve.85.046602" @default.
• W2000700975 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/22680593" @default.
• W2000700975 hasPublicationYear "2012" @default.
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