On the Integrability of Liénard systems with a strong saddle

We study the local analytic integrability for real Li\'enard systems, x=y-F(x), y= x, with F(0)=0 but F'(0)0, which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [p:-q] resonant saddles. Th...

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Detalles Bibliográficos
Autores: Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999
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:182516
Acceso en línea:https://ddd.uab.cat/record/182516
https://dx.doi.org/urn:doi:10.1016/j.aml.2017.03.004
Access Level:acceso abierto
Palabra clave:Analytic integrability
Center problem
Liénard equations
Resonant saddle
Strong saddle
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spelling On the Integrability of Liénard systems with a strong saddleGiné, Jaume|||0000-0001-7109-2553Llibre, Jaume|||0000-0002-9511-5999Analytic integrabilityCenter problemLiénard equationsResonant saddleStrong saddleWe study the local analytic integrability for real Li\'enard systems, x=y-F(x), y= x, with F(0)=0 but F'(0)0, which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [p:-q] resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the [p:-q] resonant saddle into a strong saddle. 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/182516https://dx.doi.org/urn:doi:10.1016/j.aml.2017.03.004reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1204Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-53703-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1825162026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the Integrability of Liénard systems with a strong saddle
title On the Integrability of Liénard systems with a strong saddle
spellingShingle On the Integrability of Liénard systems with a strong saddle
Giné, Jaume|||0000-0001-7109-2553
Analytic integrability
Center problem
Liénard equations
Resonant saddle
Strong saddle
title_short On the Integrability of Liénard systems with a strong saddle
title_full On the Integrability of Liénard systems with a strong saddle
title_fullStr On the Integrability of Liénard systems with a strong saddle
title_full_unstemmed On the Integrability of Liénard systems with a strong saddle
title_sort On the Integrability of Liénard systems with a strong saddle
dc.creator.none.fl_str_mv Giné, Jaume|||0000-0001-7109-2553
Llibre, Jaume|||0000-0002-9511-5999
author Giné, Jaume|||0000-0001-7109-2553
author_facet Giné, Jaume|||0000-0001-7109-2553
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Analytic integrability
Center problem
Liénard equations
Resonant saddle
Strong saddle
topic Analytic integrability
Center problem
Liénard equations
Resonant saddle
Strong saddle
description We study the local analytic integrability for real Li\'enard systems, x=y-F(x), y= x, with F(0)=0 but F'(0)0, which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [p:-q] resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the [p:-q] resonant saddle into a strong saddle.
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/182516
https://dx.doi.org/urn:doi:10.1016/j.aml.2017.03.004
url https://ddd.uab.cat/record/182516
https://dx.doi.org/urn:doi:10.1016/j.aml.2017.03.004
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1204
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-53703-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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://rightsstatements.org/vocab/InC/1.0/
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
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