Examples of center cyclicity bounds using the reduced Bautin depth

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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.date.accessioned2017-08-31T10:30:10Z
dc.date.available2017-08-31T10:30:10Z
dc.date.issued2017-09-01
dc.date.updated2017-08-31T10:30:10Z
dc.description.abstractThere is a method for bounding the cyclicity of nondegenerate monodromic singularities of polynomial planar families of vector fields Xλ which can work even in case that the Poincar´e first return map has associated a non-radical Bautin ideal B. The method is based on the stabilization of the integral closures of an ascending chain of polynomial ideals in the ring of polynomials in the parameters λ of the family that stabilizes at B. In this work we use computational algebra methods to provide an explicit example in which the classical procedure to find the Bautin depth of B fails but the new approach is successful.
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.
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1090/proc/13570
dc.identifier.idgrec024872
dc.identifier.issn0002-9939
dc.identifier.urihttp://hdl.handle.net/10459.1/60208
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1090/proc/13570
dc.relation.ispartofProceedings of the American Mathematical Society, 2017, vol. 145, p. 4363-4370
dc.rights(c) American Mathematical Society, 2017
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectCenter
dc.subjectPolynomial vector fields
dc.subjectBautin ideal
dc.subjectCyclicity
dc.subjectLimit cycle
dc.titleExamples of center cyclicity bounds using the reduced Bautin depth
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
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