Abstract
We consider a compact invariant set Λ of an expanding map of a manifoldM and give upper and lowerbounds for the Hausdorff Dimension dim H (Λ), and box dimensionsdim B (Λ) and dim B (Λ). These bounds are given in terms of the topological entropy, topological pressure, and uniform Lyapunov exponents of the map.
A measure-theoretic version of these results is also included.
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Communicated by J.-P. Eckmann
Part of this work was done when I was in the Department of Mathematics, University of Arizona.
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Hu, H. Dimensions of invariant sets of expanding maps. Commun.Math. Phys. 176, 307–320 (1996). https://doi.org/10.1007/BF02099551
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DOI: https://doi.org/10.1007/BF02099551