Integrability Conditions for Complex Homogeneous Kukles Systems

dc.contributor.authorGiné, Jaume
dc.contributor.authorValls, Claudia
dc.date.accessioned2022-01-24T09:19:52Z
dc.date.available2022-01-24T09:19:52Z
dc.date.issued2018
dc.description.abstractIn this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,...,7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.ca_ES
dc.description.sponsorshipThe first author is partially supported by a MINECO/ FEDER grant number 2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.ca_ES
dc.identifier.doihttps://doi.org/10.1080/14029251.2018.1494731
dc.identifier.idgrec027403
dc.identifier.issn1776-0852
dc.identifier.urihttp://hdl.handle.net/10459.1/72807
dc.language.isoengca_ES
dc.publisherAtlantis and Taylor & Francisca_ES
dc.relation.isformatofReproducció del document publicat a https://doi.org/10.1080/14029251.2018.1494731ca_ES
dc.relation.ispartofJournal of Nonlinear Mathematical Physics, 2018, vol. 25, núm. 3, p. 387-398ca_ES
dc.rightscc-by-nc (c) Jaume Giné, Claudia Valls, 2018ca_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_ES
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/*
dc.subjectIntegrabilityca_ES
dc.subjectComplex center-focus problemca_ES
dc.subjectSaddle constantsca_ES
dc.subjectKukles systemsca_ES
dc.subjectGröbner Basisca_ES
dc.titleIntegrability Conditions for Complex Homogeneous Kukles Systemsca_ES
dc.typeinfo:eu-repo/semantics/articleca_ES
dc.type.versioninfo:eu-repo/semantics/publishedVersionca_ES
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