Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry

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Reyes Nozaleda, Daniel and Tempesta, Piergiulio and Tondo, Giorgio (2022) Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry. Communications in nonlinear science and numerical simulation, 104 . ISSN 1007-5704

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Official URL: http://dx.doi.org/10.1016/j.cnsns.2021.106021




Abstract

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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© 2022 Elsevier
The research of D. R. N. has been supported by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades, Spain. The research of P. T. has been supported by the research project PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades, Spain. The research of G. T. has been supported by the research project FRA2020-2021, Universitadegli Studi di Trieste, Italy. P. T. is member of Gruppo Nazionale di Fisica Matematica (GNFM) of INDAM.

Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:68476
Deposited On:12 Nov 2021 19:43
Last Modified:15 Nov 2021 09:46

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