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hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorGOURMELON, Nicolas
dc.date.accessioned2024-04-04T02:28:56Z
dc.date.available2024-04-04T02:28:56Z
dc.date.created2009
dc.date.issued2010
dc.identifier.issn1078-0947
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190133
dc.description.abstractEnGiven a [C^1] -diffeomorphism [f] of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small [C^1] -perturbation that preserves the orbit of the saddle and that generates a homoclinic tangency related to it. Moreover, we show that the perturbation can be performed preserving a homoclinic relation to another saddle. We derive some consequences on homoclinic classes. In particular, if the homoclinic class of a saddle [P] has no dominated splitting of same index as [P] , then a [C^1] -perturbation generates a homoclinic tangency related to [P] .
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciences
dc.subject.enDominated splitting
dc.subject.enhomoclinic tangency
dc.subject.enbifurcation
dc.subject.enhomoclinic class.
dc.subject.enhomoclinic class
dc.title.enGeneration of homoclinic tangencies by $C^1$-perturbations.
dc.typeArticle de revue
dc.identifier.doi10.3934/dcds.2010.26.1
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
bordeaux.journalDiscrete and Continuous Dynamical Systems - Series A
bordeaux.page1-42
bordeaux.volume26
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00489042
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00489042v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20and%20Continuous%20Dynamical%20Systems%20-%20Series%20A&rft.date=2010&rft.volume=26&rft.issue=1&rft.spage=1-42&rft.epage=1-42&rft.eissn=1078-0947&rft.issn=1078-0947&rft.au=GOURMELON,%20Nicolas&rft.genre=article


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