Center problem for trigonometric Liénard systems

We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems and the characterization of some subfields of the quotient field of the ring...

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Detalles Bibliográficos
Autores: Gasull, Armengol, Giné, Jaume, Valls, Claudia
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:10459.1/62979
Acceso en línea:https://doi.org/10.1016/j.jde.2017.05.008
http://hdl.handle.net/10459.1/62979
Access Level:acceso abierto
Palabra clave:Center problem
Trigonometric Liénard equation
Trigonometric polynomial
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spelling Center problem for trigonometric Liénard systemsGasull, ArmengolGiné, JaumeValls, ClaudiaCenter problemTrigonometric Liénard equationTrigonometric polynomialWe give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems and the characterization of some subfields of the quotient field of the ring of trigonometric polynomials. Our results are also applied to some particular subfamilies of planar trigonometric Liénard systems. The results obtained are reminiscent of the ones for planar polynomial Liénard systems but the proofs are different.The first author is partially supported by the MINECO MTM2013-40998-P and the AGAUR (Generalitat de Catalunya) 2014SGR568 grants. The second author is partially supported by the MINECO/FEDER grant number MTM2014-53703-P and the AGAUR grant number 2014SGR 1204. The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013.Elsevier2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1016/j.jde.2017.05.008http://hdl.handle.net/10459.1/62979reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésMINECO/PN2013-2016/MTM2013-40998-PMINECO/PN2013-2016/MTM2014-53703-PVersió postprint del document publicat a https://doi.org/10.1016/j.jde.2017.05.008Journal of Differential Equations, 2017, vol. 263, p. 3928-3942cc-by-nc-nd (c) Elsevier, 2017info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:repositori.udl.cat:10459.1/629792026-06-24T12:42:17Z
dc.title.none.fl_str_mv Center problem for trigonometric Liénard systems
title Center problem for trigonometric Liénard systems
spellingShingle Center problem for trigonometric Liénard systems
Gasull, Armengol
Center problem
Trigonometric Liénard equation
Trigonometric polynomial
title_short Center problem for trigonometric Liénard systems
title_full Center problem for trigonometric Liénard systems
title_fullStr Center problem for trigonometric Liénard systems
title_full_unstemmed Center problem for trigonometric Liénard systems
title_sort Center problem for trigonometric Liénard systems
dc.creator.none.fl_str_mv Gasull, Armengol
Giné, Jaume
Valls, Claudia
author Gasull, Armengol
author_facet Gasull, Armengol
Giné, Jaume
Valls, Claudia
author_role author
author2 Giné, Jaume
Valls, Claudia
author2_role author
author
dc.subject.none.fl_str_mv Center problem
Trigonometric Liénard equation
Trigonometric polynomial
topic Center problem
Trigonometric Liénard equation
Trigonometric polynomial
description We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems and the characterization of some subfields of the quotient field of the ring of trigonometric polynomials. Our results are also applied to some particular subfamilies of planar trigonometric Liénard systems. The results obtained are reminiscent of the ones for planar polynomial Liénard systems but the proofs are different.
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.jde.2017.05.008
http://hdl.handle.net/10459.1/62979
url https://doi.org/10.1016/j.jde.2017.05.008
http://hdl.handle.net/10459.1/62979
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MINECO/PN2013-2016/MTM2013-40998-P
MINECO/PN2013-2016/MTM2014-53703-P
Versió postprint del document publicat a https://doi.org/10.1016/j.jde.2017.05.008
Journal of Differential Equations, 2017, vol. 263, p. 3928-3942
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/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2017
http://creativecommons.org/licenses/by-nc-nd/4.0/
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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