On the Darboux integrability of the logarithmic galactic potentials

We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. We prove that this Hamiltonian system is completely...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221289
Acceso en línea:https://ddd.uab.cat/record/221289
https://dx.doi.org/urn:doi:10.1016/j.geomphys.2017.07.019
Access Level:acceso abierto
Palabra clave:Logarithmic galactic potential
Polynomial integrability
Rational integrability
Darboux polynomials
Darboux first integrals
Invariant algebraic hypersurfaces
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spelling On the Darboux integrability of the logarithmic galactic potentialsLlibre, Jaume|||0000-0002-9511-5999Valls, Clàudia|||0000-0001-8279-1229Logarithmic galactic potentialPolynomial integrabilityRational integrabilityDarboux polynomialsDarboux first integralsInvariant algebraic hypersurfacesWe study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. We prove that this Hamiltonian system is completely integrable with Darboux first integrals if and only if q=±1. 22017-01-0120172017-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/221289https://dx.doi.org/urn:doi:10.1016/j.geomphys.2017.07.019reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 318999Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 PIV-DGR-2010open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2212892026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the Darboux integrability of the logarithmic galactic potentials
title On the Darboux integrability of the logarithmic galactic potentials
spellingShingle On the Darboux integrability of the logarithmic galactic potentials
Llibre, Jaume|||0000-0002-9511-5999
Logarithmic galactic potential
Polynomial integrability
Rational integrability
Darboux polynomials
Darboux first integrals
Invariant algebraic hypersurfaces
title_short On the Darboux integrability of the logarithmic galactic potentials
title_full On the Darboux integrability of the logarithmic galactic potentials
title_fullStr On the Darboux integrability of the logarithmic galactic potentials
title_full_unstemmed On the Darboux integrability of the logarithmic galactic potentials
title_sort On the Darboux integrability of the logarithmic galactic potentials
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Valls, Clàudia|||0000-0001-8279-1229
author2_role author
dc.subject.none.fl_str_mv Logarithmic galactic potential
Polynomial integrability
Rational integrability
Darboux polynomials
Darboux first integrals
Invariant algebraic hypersurfaces
topic Logarithmic galactic potential
Polynomial integrability
Rational integrability
Darboux polynomials
Darboux first integrals
Invariant algebraic hypersurfaces
description We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. We prove that this Hamiltonian system is completely integrable with Darboux first integrals if and only if q=±1.
publishDate 2017
dc.date.none.fl_str_mv 2
2017-01-01
2017
2017-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/221289
https://dx.doi.org/urn:doi:10.1016/j.geomphys.2017.07.019
url https://ddd.uab.cat/record/221289
https://dx.doi.org/urn:doi:10.1016/j.geomphys.2017.07.019
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 318999
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 PIV-DGR-2010
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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