Abstract
Letf be aC r diffeomorphism,r≥2, of a two dimensional manifoldM 2, and let Λ be a horseshoe off (i.e. a transitive and isolated hyperbolic set with topological dimension zero). We prove that there exist aC r neighborhoodU off and a neighbourhoodU of Λ such that forg∈U, the Hausdorff dimension of ∩ n g n(U) is aC r−1 function ofg.
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Mañé, R. The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces. Bol. Soc. Bras. Mat 20, 1–24 (1990). https://doi.org/10.1007/BF02585431
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DOI: https://doi.org/10.1007/BF02585431