%0 Journal Article
%A Reyes Nozaleda, Daniel
%A Tempesta, Piergiulio
%A Tondo, Giorgio
%T Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
%D 2022
%@ 1007-5704
%U https://hdl.handle.net/20.500.14352/72439
%X We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of (omega, H ) structures. They are symplectic manifolds en-dowed with a compatible Haantjes algebra H , namely an algebra of (1,1)tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coor-dinates, will be constructed from the Haantjes algebras associated with a separable sys-tem. These coordinates enable the additive separation of variables of the corresponding Hamilton-Jacobi equation. We shall prove that a multiseparable system admits as many omega H structures as sepa-ration coordinate systems. In particular, we will show that a large class of multiseparable, superintegrable systems, including the Smorodinsky-Winternitz systems and some physi-cally relevant systems with three degrees of freedom, possesses multiple Haantjes struc-tures. (C) 2021 Published by Elsevier B.V.
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