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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.date.accessioned2021-06-03T07:37:11Z
dc.date.issued2021-06-02
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10459.1/71375
dc.description.abstractWe consider three-dimensional polynomial families of vector fields parameterized by the admissible coefficients having a fixed zero-Hopf equilibrium and a non-singular rotation axis through it. We are interested in the periodic ν-orbits, that is, those orbits that makes a fixed arbitrary number ν (or a divisor of ν) of revolutions about the rotation axis and then returns to the initial point closing the orbit. We develop a Bautin-type method to study the ν-cyclicity of the equilibrium, that is, the maximum number of small-amplitude ν-limit cycles (isolated periodic ν-orbits) that can be made to bifurcate from the equilibrium by moving the parameters of the family restricted to some open semi-algebraic sets. The method uses branching theory based on Newton-Puiseux Theorem to get a finite number of an analytic reduced one-dimensional Poincaré maps with associated Bautin ideal on certain Noetherian ring of rational functions on an extended parameter space. We derive global upper bounds on the number of bifurcated ν-limit cycles even in the infinite codimension case for which the perturbation of a local two-dimensional invariant manifold through the singularity completely foliated by periodic ν-orbits needs to be performed. A cubic normal form serves as an example of this procedure.
dc.description.sponsorshipThe author is partially supported by a MINECO grant number MTM2017-84383-P and an AGAUR grant number 2017SGR-1276.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relationMINECO/PN2013-2016/MTM2017-84383-P
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1016/j.jde.2021.05.054
dc.relation.ispartofJournal of Differential Equations, 2021, vol. 295, p. 113-137
dc.rightscc-by-nc-nd (c) Elsevier, 2021
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es
dc.subjectZero-Hopf singularity
dc.subjectPeriodic orbits
dc.subjectPoincaré map
dc.subjectV-cyclicity
dc.titleCenter problem and ν-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2021-06-03T07:37:11Z
dc.identifier.idgrec031339
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccess
dc.identifier.doihttps://doi.org/10.1016/j.jde.2021.05.054
dc.date.embargoEndDate2023-06-02


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cc-by-nc-nd (c) Elsevier, 2021
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2021