Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry

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...

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Detalles Bibliográficos
Autores: Reyes Nozaleda, Daniel, Tempesta, Piergiulio, Tondo, Giorgio
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/72439
Acceso en línea:https://hdl.handle.net/20.500.14352/72439
Access Level:acceso abierto
Palabra clave:51-73
Física-Modelos matemáticos
Física matemática
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spelling Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometryReyes Nozaleda, DanielTempesta, PiergiulioTondo, Giorgio51-73Física-Modelos matemáticosFísica matemáticaWe 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.ElsevierUniversidad Complutense de Madrid20222022-01-0120222022-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/72439reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/724392026-06-02T12:44:21Z
dc.title.none.fl_str_mv Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
title Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
spellingShingle Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
Reyes Nozaleda, Daniel
51-73
Física-Modelos matemáticos
Física matemática
title_short Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
title_full Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
title_fullStr Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
title_full_unstemmed Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
title_sort Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
dc.creator.none.fl_str_mv Reyes Nozaleda, Daniel
Tempesta, Piergiulio
Tondo, Giorgio
author Reyes Nozaleda, Daniel
author_facet Reyes Nozaleda, Daniel
Tempesta, Piergiulio
Tondo, Giorgio
author_role author
author2 Tempesta, Piergiulio
Tondo, Giorgio
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Física-Modelos matemáticos
Física matemática
topic 51-73
Física-Modelos matemáticos
Física matemática
description 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.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/72439
url https://hdl.handle.net/20.500.14352/72439
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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