Stable sets, hyperbolicity and dimension
Rasul Shafikov Christian Wolf
Discrete & Continuous Dynamical Systems - A 2005, 12(3): 403-412 doi: 10.3934/dcds.2005.12.403
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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