Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry

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dc.contributor.authorReyes Nozaleda, Daniel
dc.contributor.authorTempesta, Piergiulio
dc.contributor.authorTondo, Giorgio
dc.date.accessioned2023-06-22T12:26:23Z
dc.date.available2023-06-22T12:26:23Z
dc.date.issued2022-01
dc.description© 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.
dc.description.abstractWe 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.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipCentros de Excelencia Severo Ochoa (MICINN)
dc.description.sponsorshipUniversitá degli Studi di Trieste
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/68476
dc.identifier.doi10.1016/j.cnsns.2021.106021
dc.identifier.issn1007-5704
dc.identifier.officialurlhttp://dx.doi.org/10.1016/j.cnsns.2021.106021
dc.identifier.relatedurlhttps://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/72439
dc.journal.titleCommunications in nonlinear science and numerical simulation
dc.language.isoeng
dc.publisherElsevier
dc.relation.projectIDPGC2018-094898-B-I00
dc.relation.projectIDCEX2019-000904-S
dc.relation.projectIDFRA2020-2021
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleClassical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
dc.typejournal article
dc.volume.number104
dspace.entity.typePublication
relation.isAuthorOfPublication971d0f71-6492-42eb-9914-45b81a7d3855
relation.isAuthorOfPublication46e9a666-a5cf-44c3-8726-7cbe2c61bd1a
relation.isAuthorOfPublication.latestForDiscovery971d0f71-6492-42eb-9914-45b81a7d3855
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