On the Integrability of Liénard systems with a strong saddle

We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ 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:...

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Detalles Bibliográficos
Autores: Giné, Jaume, Llibre, Jaume
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/62956
Acceso en línea:https://doi.org/10.1016/j.aml.2017.03.004
http://hdl.handle.net/10459.1/62956
Access Level:acceso abierto
Palabra clave:Center problem
Analytic integrability
Strong saddle
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spelling On the Integrability of Liénard systems with a strong saddleGiné, JaumeLlibre, JaumeCenter problemAnalytic integrabilityStrong saddleWe study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ 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.The first author is partially supported by a MINECO/FEDER grant number MTM2014- 53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR-1204. The second author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a MINEC0 grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568.Elsevier2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1016/j.aml.2017.03.004http://hdl.handle.net/10459.1/62956reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésMINECO/PN2013-2016/MTM2014-53703-PMINECO/PN2013-2016/MTM2013-40998-PMINECO/PN2013-2016/MTM2016-77278-PVersió postprint del document publicat a http://dx.doi.org/10.1016/j.aml.2017.03.004Applied Mathematics Letters, 2017, vol. 70, p. 39-45cc-by-nc-nd (c) Elsevier, 2017info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/3.0/esoai:repositori.udl.cat:10459.1/629562026-06-24T12:42:17Z
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
Center problem
Analytic integrability
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
Llibre, Jaume
author Giné, Jaume
author_facet Giné, Jaume
Llibre, Jaume
author_role author
author2 Llibre, Jaume
author2_role author
dc.subject.none.fl_str_mv Center problem
Analytic integrability
Strong saddle
topic Center problem
Analytic integrability
Strong saddle
description We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ 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 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1016/j.aml.2017.03.004
http://hdl.handle.net/10459.1/62956
url https://doi.org/10.1016/j.aml.2017.03.004
http://hdl.handle.net/10459.1/62956
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MINECO/PN2013-2016/MTM2014-53703-P
MINECO/PN2013-2016/MTM2013-40998-P
MINECO/PN2013-2016/MTM2016-77278-P
Versió postprint del document publicat a http://dx.doi.org/10.1016/j.aml.2017.03.004
Applied Mathematics Letters, 2017, vol. 70, p. 39-45
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2017
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/3.0/es
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es
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:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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