A C^1 -Generic dichotomy for diffeomorphisms

dc.creatorBonatti, C.
dc.creatorDiaz, L. J.
dc.creatorPujals, E. R.
dc.date2006-10-17
dc.date.accessioned2026-07-07T07:29:09Z
dc.date.available2026-07-07T07:29:09Z
dc.descriptionWe show that, for every compact n-dimensional manifold, n\geq 1, there is a residual subset of Diff^1(M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Mane [Ma3}). In particular, we show that any C^1 -robustly transitive diffeomorphism admits a dominated splitting.
dc.description64 pages, published version
dc.identifierhttps://arxiv.org/abs/math/0610527
dc.identifierhttp://arxiv.org/abs/math/0610527
dc.identifierAnn. of Math. (2), vol. 158 (2003), no.2, 355--418
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117996
dc.subjectDynamical Systems
dc.titleA C^1 -Generic dichotomy for diffeomorphisms
dc.typetext

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