Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry

We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-t...

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Detalles Bibliográficos
Autores: Kubů, O., Reyes, D., Tempesta, P., Tondo, G.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/379000
Acceso en línea:http://hdl.handle.net/10261/379000
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85209698783&doi=10.1098%2frspa.2024.0076&partnerID=40&md5=788596c1a87ece0f865253eab92355db
Access Level:acceso abierto
Palabra clave:Haantjes geometry
integrable systems
magnetic systems
Stäckel systems
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spelling Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometryKubů, O.Reyes, D.Tempesta, P.Tondo, G.Haantjes geometryintegrable systemsmagnetic systemsStäckel systemsWe investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically. In addition, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field. © 2024 The Author(s).O.K. was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS22/178/OHK4/3T/14. D.R.N. acknowledges the financial support of EXINA S.L. The research of P.T. has been supported by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovación y Universidades y Agencia Estatal de Investigación, Spain.Peer reviewedMinisterio de Ciencia e Innovación (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/379000https://www.scopus.com/inward/record.uri?eid=2-s2.0-85209698783&doi=10.1098%2frspa.2024.0076&partnerID=40&md5=788596c1a87ece0f865253eab92355dbreponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésProceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesSíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3790002026-05-22T06:33:51Z
dc.title.none.fl_str_mv Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
title Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
spellingShingle Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
Kubů, O.
Haantjes geometry
integrable systems
magnetic systems
Stäckel systems
title_short Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
title_full Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
title_fullStr Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
title_full_unstemmed Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
title_sort Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
dc.creator.none.fl_str_mv Kubů, O.
Reyes, D.
Tempesta, P.
Tondo, G.
author Kubů, O.
author_facet Kubů, O.
Reyes, D.
Tempesta, P.
Tondo, G.
author_role author
author2 Reyes, D.
Tempesta, P.
Tondo, G.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Haantjes geometry
integrable systems
magnetic systems
Stäckel systems
topic Haantjes geometry
integrable systems
magnetic systems
Stäckel systems
description We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically. In addition, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field. © 2024 The Author(s).
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/379000
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85209698783&doi=10.1098%2frspa.2024.0076&partnerID=40&md5=788596c1a87ece0f865253eab92355db
url http://hdl.handle.net/10261/379000
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85209698783&doi=10.1098%2frspa.2024.0076&partnerID=40&md5=788596c1a87ece0f865253eab92355db
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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