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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.contributor.authorMaza Sabido, Susanna
dc.contributor.authorShafer, Douglas S.
dc.date.accessioned2018-12-10T08:40:24Z
dc.date.available2020-12-05T23:12:39Z
dc.date.issued2018-11-09
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10459.1/65279
dc.description.abstractWe consider polynomial families of ordinary differential equations on $\R^3$, parametrized by the admissible coefficients, for which the origin is an isolated singularity at which the linear part of the system has one non-zero real and two purely imaginary eigenvalues. We derive theorems that bound the maximum number of limit cycles within the center manifold that can bifurcate, under arbitrarily small perturbation of the coefficients, from any center at the origin. The bounds are global in that they apply to the system corresponding to any point on any irreducible component of the center variety in the space of parameters. We also derive theorems for such bounds when attention is confined to a single irreducible component of the center variety.
dc.description.sponsorshipThe first and second authors are partially supported by a MEC grant number MTM2016- 80276-P and by a CIRIT grant number 2014 SGR 1204.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relationMINECO/PN2013-2016/MTM2016-80276-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1016/j.jde.2018.07.019
dc.relation.ispartofJournal of Differential Equations, 2018, vol. 265, p. 5767-5808
dc.rightscc-by-nc-nd (c) Elsevier, 2018
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es
dc.subjectCyclicity
dc.subjectLimit cycle
dc.subjectCenter manifold
dc.titleCyclicity of polynomial nondegenerate centers on center manifolds
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2018-12-10T08:40:26Z
dc.identifier.idgrec027818
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1016/j.jde.2018.07.019


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cc-by-nc-nd (c) Elsevier, 2018
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2018