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Stable sets, hyperbolicity and dimension

Rasul Shafikov·Christian Wolf
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Abstract

In this note we derive an upper bound for the Hausdorff dimension of the stable set of a hyperbolic set $Λ$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold. As a consequence we obtain that $\dim_H W^s(Λ)=n$ is equivalent to the existence of a SRB-measure. We also discuss related results in the case of expanding maps.

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Rasul Shafikov, Christian Wolf. 2003-06-19. Stable sets, hyperbolicity and dimension. https://arxiv.org/abs/math/0306282

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