Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/101972
Author(s): Pinto, AA
Rand, DA
Ferreira, E
Title: Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
Issue Date: 2007
Abstract: We prove that the stable holonomies of a proper codimension 1 attractor Lambda, for a C-r diffeomorphism f of a surface, are not C1+theta for theta greater than the Hausdorff dimension of the stable leaves of f intersected with Lambda. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.
Description: We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a C^r diffeomorphism fof a surface, are not C^{1+θ} for θ greater than the Hausdorff dimension of the stable leaves of f intersectedwith Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on theattractor.
Subject: Matemática
Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://repositorio-aberto.up.pt/handle/10216/101972
Document Type: Artigo em Revista Científica Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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