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Expansiveness, hyperbolicity and Hausdorff dimension

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Abstract

We show that there exists a simple upper bound on the dimension of a hyperbolic compact set of a dynamical system in terms of topological entropy and a uniform contraction rate on the stable and unstable manifolds. This allows us to give proofs of several apparently unrelated theorems.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, Florida, USA

    Albert Fathi

  2. CNRS UA1169, Université Paris-Sud, F-91405, Orsay, France

    Albert Fathi

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  1. Albert Fathi
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Communicated by J. N. Mather

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Fathi, A. Expansiveness, hyperbolicity and Hausdorff dimension. Commun.Math. Phys. 126, 249–262 (1989). https://doi.org/10.1007/BF02125125

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  • DOI: https://doi.org/10.1007/BF02125125

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