Averaging theory at any order for computing periodic orbits

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dc.contributor.authorGiné, Jaume
dc.contributor.authorGrau Montaña, Maite
dc.contributor.authorLlibre, Jaume
dc.date.accessioned2016-02-04T09:18:19Z
dc.date.available2016-02-04T09:18:19Z
dc.date.issued2013-05
dc.date.updated2016-02-04T09:10:02Z
dc.description.abstractWe provide a recurrence formula for the coefficients of the powers of ε in the series expansion of the solutions around ε=0 of the perturbed first-order differential equations. Using it, we give an averaging theory at any order in εε for the following two kinds of analytic differential equation: A planar polynomial differential system with a singular point at the origin can be transformed, using polar coordinates, to an equation of the previous form. Thus, we apply our results for studying the limit cycles of a planar polynomial differential systems.ca_ES
dc.description.sponsorshipThe first and second authors are partially supported by a MICINN/FEDER grant number MTM2011-22877 and by a Generalitat de Catalunya grant number 2009SGR 381. The third author is partially supported by a MICINN/ FEDER grant number MTM2008-03437, by a Generalitat de Catalunya grant number 2009SGR 410 and by ICREA Academiaca_ES
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1016/j.physd.2013.01.015
dc.identifier.idgrec019197
dc.identifier.issn0167-2789
dc.identifier.urihttp://hdl.handle.net/10459.1/49442
dc.language.isoengca_ES
dc.publisherElsevierca_ES
dc.relationMICINN/PN2008-2011/MTM2011-22877ca_ES
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1016/j.physd.2013.01.015ca_ES
dc.relation.ispartofPhysica D, 2013, vol. 250, p. 58-65ca_ES
dc.rightscc-by-nc-nd(c) Elsevier, 2013ca_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_ES
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca
dc.subjectFirst-order analytic differential equationsca_ES
dc.subjectAveraging theoryca_ES
dc.subjectPolynomial differential equationsca_ES
dc.subjectLimit cyclesca_ES
dc.subjectPeriodic orbitsca_ES
dc.subject.otherEquacions diferencialsca_ES
dc.subject.otherÒrbites periòdiquesca_ES
dc.titleAveraging theory at any order for computing periodic orbitsca_ES
dc.typearticleca_ES
dc.type.versionacceptedVersionca_ES
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