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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.date.accessioned2016-05-20T15:37:58Z
dc.date.issued2016
dc.identifier.issn0002-9939
dc.identifier.urihttp://hdl.handle.net/10459.1/57073
dc.description.abstractWe describe a method for bounding the cyclicity of the class of monodromic singularities of polyn omial planar families of vector fields X λ with an analytic Poincar e first return map having a polynomial Bautin ideal B in the ring of polynomials in the parameters λ of the family. This class includes the nondegenerate centers, generic nilpotent centers and also some degenerate centers. This method can work even in the case in which B is not radical by studying the stabilization of the integral closures of an ascending chain of polynomial ideals that stabilizes at B. The approach is based on computational algebra methods for determining a minimal basis of the integral closurē B of B. As far as we know, the obtained cyclicity bound is the minimum found in the literature.ca_ES
dc.description.sponsorshipThe first author was partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204.ca_ES
dc.language.isoengca_ES
dc.publisherAmerican Mathematical Societyca_ES
dc.relationMINECO/PN2013-2016/MTM2014-53703-Pca_ES
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1090/proc/12896ca_ES
dc.relation.ispartofProceedings of the American Mathematical Society, 2016, vol. 144, núm. 6, p. 2473–2478ca_ES
dc.rights(c) American Mathematical Society, 2016ca_ES
dc.subjectCenterca_ES
dc.subjectPolynomial vector fieldsca_ES
dc.subjectBautin idealca_ES
dc.subjectCyclicityca_ES
dc.subjectLimit cycleca_ES
dc.titleThe cyclicity of polynomial centers via the reduced bautin depthca_ES
dc.typearticleca_ES
dc.identifier.idgrec023235
dc.type.versionacceptedVersionca_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1090/proc/12896


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