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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.date.accessioned2016-11-03T09:39:47Z
dc.date.available2017-02-01T23:51:56Z
dc.date.issued2016
dc.identifier.issn0218-1274
dc.identifier.urihttp://hdl.handle.net/10459.1/58362
dc.description.abstractWe are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to characterize such a centers we use a more general object, namely, formal inverse integrating factors V of X. Although by the existence of V is not possible to describe all nilpotent centers strata, we simplify, improve and also extend previous results on the relationship between these concepts. We use in the performed analysis the so-called Andreev number n N with n > 2 associated to X which is invariant under orbital conjugacy of X. Besides the leading terms in the (1,n)-quasihomogeneous expansions that V can have we also prove the following: (i) If n is even and there exists V then X has a center; (iii) If the existence of V characterizes all the centers; (iii) If there is a V with minimum ``vanishing multiplicity' at the singularity then, generically, X has a center.
dc.description.sponsorshipThe 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.language.isoeng
dc.publisherWorld Scientific Publishing
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1142/S0218127416500152
dc.relation.ispartofInternational Journal of Bifurcation and Chaos, 2016, vol. 26, p. 1650015-1-1650015-13
dc.rights(c) World Scientific Publishing, 2016
dc.subjectMonodromic singularity
dc.subjectNilpotent center
dc.subjectIntegrability
dc.subjectInverse integrating factor
dc.titleFormal inverse integrating factors and the nilpotent center problem
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2016-11-03T09:39:49Z
dc.identifier.idgrec024028
dc.type.versionacceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1142/S0218127416500152


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