A sufficient condition in order that the real Jacobian conjecture in R^2 holds

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dc.contributor.authorBraun, Francisco
dc.contributor.authorGiné, Jaume
dc.contributor.authorLlibre, Jaume
dc.date.accessioned2016-11-04T13:00:55Z
dc.date.available2018-04-01T22:14:38Z
dc.date.issued2016
dc.date.updated2016-11-04T13:00:56Z
dc.description.abstractLet F=(f,g):R2→R2 be a polynomial map such that det⁡DF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of the polynomials ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.
dc.description.sponsorshipThe first author is partially supported by a BPE-FAPESP grant number 2014/26149-3. The second author is partially supported by a MINECO/FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The third author is partially supported by a MINECO grant number MTM2013- 40998-P, and AGAUR grant number 2014SGR 568 and two FP7-PEOPLE- 2012-IRSES grants numbers 316338 and 318999. The first and the third author are also partially supported by a CAPES CSF–PVE grant 88881. 030454/ 2013-01 from the program CSF-PVE.
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1016/j.jde.2015.12.011
dc.identifier.idgrec023781
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10459.1/58388
dc.language.isoeng
dc.publisherElsevier
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relationMINECO/PN2013-2016/MTM2013-40998-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1016/j.jde.2015.12.011
dc.relation.ispartofJournal of Differential Equations, 2016, vol. 260, num. 6, p. 5250-5258
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/318999
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/316338
dc.rightscc-by-nc-nd (c) Elsevier, 2016
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectReal Jacobian conjecture
dc.subjectGlobal injectivity
dc.subjectCentre
dc.titleA sufficient condition in order that the real Jacobian conjecture in R^2 holds
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
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