Abstract
We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a C r diffeomorphism f of a surface, are not C 1 + θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. 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.
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