Stable sets, hyperbolicity and dimension

Rasul Shafikov; Christian Wolf

Stable sets, hyperbolicity and dimension

Dynamical Systems 2007-05-23 v1

Authors: Rasul Shafikov , Christian Wolf

Abstract

In this note we derive an upper bound for the Hausdorff dimension of the 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 in the case of expanding maps.

Keywords

hausdorff dimension hausdorff measure and dimension partially hyperbolic dynamics

Cite

@article{arxiv.math/0306282,
  title  = {Stable sets, hyperbolicity and dimension},
  author = {Rasul Shafikov and Christian Wolf},
  journal= {arXiv preprint arXiv:math/0306282},
  year   = {2007}
}

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