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dc.contributor.authorGiné, Jaume
dc.contributor.authorLlibre, Jaume
dc.contributor.authorValls, Claudia
dc.date.accessioned2016-11-04T17:37:51Z
dc.date.available2016-11-04T17:37:51Z
dc.date.issued2015
dc.identifier.issn0024-6093
dc.identifier.urihttp://hdl.handle.net/10459.1/58395
dc.description.abstractFor the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done 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.
dc.description.sponsorshipThe first author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO/FEDER grant MTM2008-03437 and MTM2013-40998-P, an AGAUR grant number 2014 SGR568, an ICREA Academia, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338, FEDER-UNAB-10-4E-378. The third author is supported by Portuguese National Funds through FCT – Fundação para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherLondon Mathematical Society
dc.relationinfo:eu-repo/grantAgreement/MICINN//MTM2011-22877/ES/BIFURCACIONES, INTEGRABILIDAD Y PROPIEDADES CUALITATIVAS DE FAMILIAS DE CAMPOS VECTORIALES/
dc.relationinfo:eu-repo/grantAgreement/MICINN//MTM2008-03437/ES/ORBITAS PERIODICAS, BIFURCACIONES E INTEGRABILIDAD DE LOS SISTEMAS DINAMICOS/
dc.relationinfo:eu-repo/grantAgreement/MINECO//MTM2013-40998-P/ES/ALGUNOS ASPECTOS DE LA DINAMICA GLOBAL DE LOS SISTEMAS DIFERENCIALES: INTEGRABILIDAD, SOLUCIONES PERIODICAS Y BIFURCACIONES/
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1112/blms/bdv005
dc.relation.ispartofBulletin of the London Mathematical Society, 2015, vol. 47, p. 315-324
dc.rights(c) London Mathematical Society, 2015
dc.subjectIntegrability
dc.subjectComplex center-focus problem
dc.subjectLyapunov constants
dc.subjectBautin method
dc.subject.classificationMatemàtica
dc.subject.otherMathematics
dc.titleCenters for the Kukles homogeneous systems with odd degree
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2016-11-04T17:37:51Z
dc.identifier.idgrec023249
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1112/blms/bdv005
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/318999
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/316338


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