Centers for the Kukles homogeneous systems with odd degree

For the polynomial differential system x ̇ = -y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetri...

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Autores: Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:145329
Acesso em linha:https://ddd.uab.cat/record/145329
https://dx.doi.org/urn:doi:10.1112/blms/bdv005
Access Level:acceso abierto
Palavra-chave:Bautin method
Complex center-focus problem
Lyapunov constants
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spelling Centers for the Kukles homogeneous systems with odd degreeGiné, Jaume|||0000-0001-7109-2553Llibre, Jaume|||0000-0002-9511-5999Valls, Clàudia|||0000-0001-8279-1229Bautin methodComplex center-focus problemLyapunov constantsFor the polynomial differential system x ̇ = -y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We prove both conjectures for all n odd. 22015-01-0120152015-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/145329https://dx.doi.org/urn:doi:10.1112/blms/bdv005reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-22877Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Ministerio 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-1204European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 318999open 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:1453292026-06-06T12:50:31Z
dc.title.none.fl_str_mv Centers for the Kukles homogeneous systems with odd degree
title Centers for the Kukles homogeneous systems with odd degree
spellingShingle Centers for the Kukles homogeneous systems with odd degree
Giné, Jaume|||0000-0001-7109-2553
Bautin method
Complex center-focus problem
Lyapunov constants
title_short Centers for the Kukles homogeneous systems with odd degree
title_full Centers for the Kukles homogeneous systems with odd degree
title_fullStr Centers for the Kukles homogeneous systems with odd degree
title_full_unstemmed Centers for the Kukles homogeneous systems with odd degree
title_sort Centers for the Kukles homogeneous systems with odd degree
dc.creator.none.fl_str_mv Giné, Jaume|||0000-0001-7109-2553
Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author Giné, Jaume|||0000-0001-7109-2553
author_facet Giné, Jaume|||0000-0001-7109-2553
Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author2_role author
author
dc.subject.none.fl_str_mv Bautin method
Complex center-focus problem
Lyapunov constants
topic Bautin method
Complex center-focus problem
Lyapunov constants
description For the polynomial differential system x ̇ = -y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We prove both conjectures for all n odd.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
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/145329
https://dx.doi.org/urn:doi:10.1112/blms/bdv005
url https://ddd.uab.cat/record/145329
https://dx.doi.org/urn:doi:10.1112/blms/bdv005
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-22877
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
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
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 318999
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
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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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