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hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierInstituto Nacional de Matemática Pura e Aplicada [IMPA]
dc.contributor.authorGOURMELON, Nicolas
dc.date.accessioned2024-04-04T02:23:23Z
dc.date.available2024-04-04T02:23:23Z
dc.date.created2012-12-26
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189735
dc.description.abstractEnA well-known lemma by John Franks asserts that one obtains any perturbation of the derivative of a diffeomorphism along a periodic orbit by a $C^1$-perturbation of the whole diffeomorphism on a small neighbourhood of the orbit. However, one does not control where the invariant manifolds of the orbit are, after perturbation. We show that if the perturbated derivative is obtained by an isotopy along which some strong stable/unstable manifolds of some dimensions exist, then the Franks perturbation can be done preserving the corresponding stable/unstable semi-local manifolds. This is a general perturbative tool in $C^1$-dynamics that has many consequences. We give simple examples of such consequences, for instance a generic dichotomy between dominated splitting and small stable/unstable angles inside homoclinic classes.
dc.language.isoen
dc.subject.enFranks Lemma
dc.subject.enperiodic point
dc.subject.ensaddle point
dc.subject.enlinear cocycle
dc.subject.enperturbation
dc.subject.enstable/unstable manifold
dc.subject.endominated splitting
dc.subject.enhomoclinic tangency
dc.subject.ensmall angles
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.identifier.arxiv1212.6638
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00769205
hal.version1
hal.audienceNon spécifiée
dc.title.itAn Isotopic Perturbation Lemma Along Periodic Orbits
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00769205v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GOURMELON,%20Nicolas&rft.genre=preprint


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