Stable sets, hyperbolicity and dimension
Rasul Shafikov Christian Wolf
In this note we derive an upper bound for the Hausdorff and box dimension of the stable and local stable set of a hyperbolic set $\Lambda$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold. As a consequence we obtain that dim$_H W^s(\Lambda)=n$ is equivalent to the existence of a SRB-measure. We also discuss related results for expanding maps.
keywords: box dimension stable sets. SRB measure Hausdorff dimension Hyperbolic sets

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