Center cyclicity of a family of quartic polynomial differential system

In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we p...

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Detalles Bibliográficos
Autores: García, I. A. (Isaac A.), Llibre, Jaume, Maza Sabido, Susanna
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/58372
Acceso en línea:https://doi.org/10.1007/s00030-016-0388-8
http://hdl.handle.net/10459.1/58372
Access Level:acceso abierto
Palabra clave:Center
Polynomial vector fields
Bautin ideal
Cyclicity
Limit cycle
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spelling Center cyclicity of a family of quartic polynomial differential systemGarcía, I. A. (Isaac A.)Llibre, JaumeMaza Sabido, SusannaCenterPolynomial vector fieldsBautin idealCyclicityLimit cycleIn this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.The first and third authors are partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant number 2014SGR 568, two FP7-PEOPLE-2012-IRSES numbers 316338 and 318999.Springer2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1007/s00030-016-0388-8http://hdl.handle.net/10459.1/58372reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésMINECO/PN2013-2016/MTM2014-53703-PMINECO/PN2013-2016/MTM2013-40998-PVersió postprint del document publicat a https://doi.org/10.1007/s00030-016-0388-8Nonlinear Differential Equations and Applications-NoDEA, 2016, vol. 23, n. 34info:eu-repo/grantAgreement/EC/FP7/318999info:eu-repo/grantAgreement/EC/FP7/316338(c) Springer, 2016info:eu-repo/semantics/openAccessoai:recercat.cat:10459.1/583722026-05-29T05:05:01Z
dc.title.none.fl_str_mv Center cyclicity of a family of quartic polynomial differential system
title Center cyclicity of a family of quartic polynomial differential system
spellingShingle Center cyclicity of a family of quartic polynomial differential system
García, I. A. (Isaac A.)
Center
Polynomial vector fields
Bautin ideal
Cyclicity
Limit cycle
title_short Center cyclicity of a family of quartic polynomial differential system
title_full Center cyclicity of a family of quartic polynomial differential system
title_fullStr Center cyclicity of a family of quartic polynomial differential system
title_full_unstemmed Center cyclicity of a family of quartic polynomial differential system
title_sort Center cyclicity of a family of quartic polynomial differential system
dc.creator.none.fl_str_mv García, I. A. (Isaac A.)
Llibre, Jaume
Maza Sabido, Susanna
author García, I. A. (Isaac A.)
author_facet García, I. A. (Isaac A.)
Llibre, Jaume
Maza Sabido, Susanna
author_role author
author2 Llibre, Jaume
Maza Sabido, Susanna
author2_role author
author
dc.subject.none.fl_str_mv Center
Polynomial vector fields
Bautin ideal
Cyclicity
Limit cycle
topic Center
Polynomial vector fields
Bautin ideal
Cyclicity
Limit cycle
description In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.
publishDate 2016
dc.date.none.fl_str_mv 2016
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/10.1007/s00030-016-0388-8
http://hdl.handle.net/10459.1/58372
url https://doi.org/10.1007/s00030-016-0388-8
http://hdl.handle.net/10459.1/58372
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
Versió postprint del document publicat a https://doi.org/10.1007/s00030-016-0388-8
Nonlinear Differential Equations and Applications-NoDEA, 2016, vol. 23, n. 34
info:eu-repo/grantAgreement/EC/FP7/318999
info:eu-repo/grantAgreement/EC/FP7/316338
dc.rights.none.fl_str_mv (c) Springer, 2016
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer, 2016
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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