Stable sets, hyperbolicity and dimension

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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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Dynamical Systems, 37C45; 37DXX

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http://salesiana.dossiersoluciones.com/handle/123456789/67829

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306282
 http://arxiv.org/abs/math/0306282

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arXiv