Stable sets, hyperbolicity and dimension

2003/06/19 by Rasul Shafikov, Christian Wolf, Shafikov, Rasul +1
Mathematics · Physics and Astronomy · #37C45 #37DXX #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C45 #msc:37DXX

paper · pdf · doi:10.48550/arxiv.math/0306282

arxiv created 2003/06/19 · openalex publication_date 2003/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we derive an upper bound for the Hausdorff dimension of the stable set of a hyperbolic set Λ of a C² 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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