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dc.contributor.authorGasull i Embid, Armengol
dc.contributor.authorGiné, Jaume
dc.contributor.authorTorregrosa, Joan
dc.date.accessioned2016-11-07T17:28:32Z
dc.date.issued2016
dc.identifier.issn1534-0392
dc.identifier.urihttp://hdl.handle.net/10459.1/58414
dc.description.abstractWe study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. To the best of our knowledge this list includes a new class of Darboux centers that are also persistent centers. The rest of the paper is dedicated to try to prove that the given list is exhaustive. We get several partial results that seem to indicate that this is the case. In particular, we solve the question for several general families with arbitrary high degree and for all cases of degree less or equal than 19. As a byproduct of our study we also obtain the highest known order for weak-foci of planar polynomial systems of some given degrees.
dc.description.sponsorshipThe first and third authors are partially supported by the MINECO MTM2013-40998-P grant, the MINECO/FEDERUNAB13-4E-1604 grant and the AGAUR (Generalitat de Catalunya) 2014SGR568 grant. The second author is partially supported by the MINECO MTM2014-53703-P grant and the AGAUR (Generalitat de Catalunya) 2014SGR1204 grant.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.relationMINECO/PN2013-2016/MTM2013-40998-P
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relation.isformatofReproducció del document publicat a: https://doi.org/10.3934/cpaa.2016.15.577
dc.relation.ispartofCommunications on Pure and Applied Analysis, 2016, vol. 15, núm. 2, p. 577-598
dc.rights(c) American Institute of Mathematical Sciences, 2016
dc.subjectNondegenerate center
dc.subjectPoincaré--Lyapunov constants
dc.subjectDarboux center
dc.subjectReversible center
dc.subjectHolomorphic center
dc.subjectPersistent center
dc.subject.classificationMatemàtica
dc.subject.otherMathematics
dc.titleCenter problem for systems with two monomial nonlinearities
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2016-11-07T17:28:32Z
dc.identifier.idgrec023780
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/restrictedAccess
dc.identifier.doihttps://doi.org/10.3934/cpaa.2016.15.577
dc.date.embargoEndDate10000-01-01


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