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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.contributor.authorValls, Claudia
dc.date.accessioned2016-11-08T14:28:10Z
dc.date.issued2016-03-01
dc.identifier.issn1078-0947
dc.identifier.urihttp://hdl.handle.net/10459.1/58428
dc.description.abstractIn this work we extend well-known techniques for solving the Poincar\'e-Lyapunov nondegenerate analytic center problem in the plane to the 3-dimensional center problem at the zero-Hopf singularity. Thus we characterize the existence of a neighborhood of the singularity completely foliated by periodic orbits (including continua of equilibria) via an analytic Poincar\'e return map. The vanishing of the first terms in a Taylor expansion of the associated displacement map provides us with the necessary 3-dimensional center conditions in the parameter space of the family whereas the sufficiency is obtained through symmetry-integrability methods. Finally we use the proposed method to classify the 3-dimensional centers of some quadratic polynomial differential families possessing a zero-Hopf singularity.
dc.description.sponsorshipThe first author is 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 Portuguese national funds through FCT - Fundaçao para a Ciéncia e a Tecnologia: project UID/MAT/04459/2013 (CAMGSD).
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.3934/dcds.2016.36.2027
dc.relation.ispartofDiscrete and Continuous Dynamical Systems Series A, 2016, vol. 36, núm. 4, p. 2027-2046
dc.rights(c) American Institute of Mathematical Sciences , 2016
dc.subjectZero-Hopf singularity
dc.subjectThree-dimensional vector fields
dc.subjectContinua of periodic orbits
dc.subjectPoincaré map
dc.subject.classificationMatemàtica
dc.subject.otherMathematics
dc.titleThe three-dimensional center problem for the zero-Hopf singularity
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2016-11-08T14:28:10Z
dc.identifier.idgrec023236
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.3934/dcds.2016.36.2027


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