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 \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C 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 t...

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Detalles Bibliográficos
Autores: García, Isaac|||0000-0001-6982-9632, Llibre, Jaume|||0000-0002-9511-5999, Maza, Susanna|||0000-0001-9488-5644
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169476
Acceso en línea:https://ddd.uab.cat/record/169476
https://dx.doi.org/urn:doi:10.1007/s00030-016-0388-8
Access Level:acceso abierto
Palabra clave:Algebraic limit cycles
Bautin ideal
Center
Cyclicity
Polynomial vector fields
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spelling Center cyclicity of a family of quartic polynomial differential systemGarcía, Isaac|||0000-0001-6982-9632Llibre, Jaume|||0000-0002-9511-5999Maza, Susanna|||0000-0001-9488-5644Algebraic limit cyclesBautin idealCenterCyclicityPolynomial vector fieldsIn this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C 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. 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/169476https://dx.doi.org/urn:doi:10.1007/s00030-016-0388-8reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio 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-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1204Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 316339open 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:1694762026-06-06T12:50:31Z
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, Isaac|||0000-0001-6982-9632
Algebraic limit cycles
Bautin ideal
Center
Cyclicity
Polynomial vector fields
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, Isaac|||0000-0001-6982-9632
Llibre, Jaume|||0000-0002-9511-5999
Maza, Susanna|||0000-0001-9488-5644
author García, Isaac|||0000-0001-6982-9632
author_facet García, Isaac|||0000-0001-6982-9632
Llibre, Jaume|||0000-0002-9511-5999
Maza, Susanna|||0000-0001-9488-5644
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Maza, Susanna|||0000-0001-9488-5644
author2_role author
author
dc.subject.none.fl_str_mv Algebraic limit cycles
Bautin ideal
Center
Cyclicity
Polynomial vector fields
topic Algebraic limit cycles
Bautin ideal
Center
Cyclicity
Polynomial vector fields
description In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C 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 2
2016-01-01
2016
2016-01-01
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/169476
https://dx.doi.org/urn:doi:10.1007/s00030-016-0388-8
url https://ddd.uab.cat/record/169476
https://dx.doi.org/urn:doi:10.1007/s00030-016-0388-8
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv 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
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1204
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 316339
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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