Centers for generalized quintic polynomial differential systems

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dc.contributor.authorGiné, Jaume
dc.contributor.authorLlibre, Jaume
dc.contributor.authorValls, Claudia
dc.date.accessioned2017-10-31T13:53:48Z
dc.date.available2017-10-31T13:53:48Z
dc.date.issued2017
dc.date.updated2017-10-31T13:53:48Z
dc.description.abstractWe classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 + F \bar z^5)$, where $A,B,C,D,E, F \in mathbb{C}$ and either $A = Re(D) = 0$, $A = Im(D) = 0$, $Re(A) = D = 0$ or $Im(A) = D = 0$.
dc.description.sponsorshipWe thank to Professor Colin Christopher for his help in the proof of statement (g) of Theorem 3. The first author is partially supported by a MINECO/ FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO/ FEDER grant number MTM2008-03437, an AGAUR grant number 2009SGR 410, ICREA Academia, two FP7-PEOPLE-2012-IRSES numbers 316338 and 318999, and FEDERUNAB10-4E-378. The third author is partially supported by FCT/Portugal through the project UID/MAT/04459/2013.
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1216/RMJ-2017-47-4-1097
dc.identifier.idgrec026049
dc.identifier.issn0035-7596
dc.identifier.urihttp://hdl.handle.net/10459.1/60411
dc.language.isoeng
dc.publisherRocky Mountain Mathematics Consortium
dc.relationinfo:eu-repo/grantAgreement/MINECO//MTM2014-53703-P/ES/METODOS CUALITATIVOS EN SISTEMAS DIFERENCIALES CONTINUOS/
dc.relationinfo:eu-repo/grantAgreement/MICINN//MTM2008-03437/ES/ORBITAS PERIODICAS, BIFURCACIONES E INTEGRABILIDAD DE LOS SISTEMAS DINAMICOS/
dc.relation.isformatofVersió preprint del document publicat a: https://doi.org/10.1216/RMJ-2017-47-4-1097
dc.relation.ispartofRocky Mountain Journal of Mathematics, 2017, vol. 47, núm. 4, p. 1097-1120
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/318999
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/316338
dc.rights(c) Rocky Mountain Mathematics Consortium, 2017
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectNilpotent center
dc.subjectDegenerate center
dc.subjectLyapunov constants
dc.subjectBautin method
dc.subject.classificationMatemàtica
dc.subject.otherMathematics
dc.titleCenters for generalized quintic polynomial differential systems
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/submittedVersion
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