Show simple item record

dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.contributor.authorLlibre, Jaume
dc.contributor.authorMaza Sabido, Susanna
dc.date.accessioned2016-11-03T12:45:14Z
dc.date.available2017-04-01T23:26:07Z
dc.date.issued2015-01-20
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10459.1/58370
dc.description.abstractWe consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the Hopf cyclicity less than or equal to the Bautin depth of B. We also present a method for studying the cyclicity problem for the Hamiltonian and the time-reversible centers without the necessity of solving previously the Dulac complex center problem associated to the larger complexified family. As application we analyze the Hopf cyclicity of the quintic polynomial family written in complex notation as z = i z + zz (A z^3 + B z^2 z + C z z2 + D z3.
dc.description.sponsorshipThe first and third authors are partially supported by a MINECO grant number MTM2011-22877 and by a CIRIT grant number 2014 SGR 1204. The second author is partially supported by a MINECO/ FEDER grants numbers MTM2008-03437 and MTM2013-40998-P, an AGAUR grant number 2014SGR 568, ICREA Academia, two FP7- PEOPLE-2012-IRSES numbers 316338 and 318999, and FEDER-UNAB10- 4E-378.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relationMICINN/PN2008-2011/MTM2011-22877
dc.relationMICINN/PN2008-2011/MTM2008-03437
dc.relationMINECO/PN2013-2016/MTM2013-40998-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1016/j.jde.2014.11.018
dc.relation.ispartofJournal of Differential Equations, 2015, vol. 258, p. 1990-2009
dc.rightscc-by-nc-nd (c) Elsevier, 2015
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectCenter
dc.subjectPolynomial vector fields
dc.subjectBautin ideal
dc.subjectCyclicity
dc.subjectLimit cycle
dc.titleThe Hopf cyclicity of the centers of a class of quintic polynomial vector fields
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2016-11-03T12:45:15Z
dc.identifier.idgrec022249
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1016/j.jde.2014.11.018
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/318999
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/316338


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

cc-by-nc-nd (c) Elsevier, 2015
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2015