# American Institute of Mathematical Sciences

April  2005, 12(3): 403-412. doi: 10.3934/dcds.2005.12.403

## Stable sets, hyperbolicity and dimension

 1 Department of Mathematics, Middlesex College, The University of Western Ontario, London, Ontario N6A 5B7, Canada 2 Department of Mathematics, Wichita State University, Wichita, Kansas, 67260, United States

Received  September 2003 Revised  August 2004 Published  December 2004

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