Dimensions of invariant sets of expanding maps |
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Authors: | Huyi Hu |
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Affiliation: | (1) Department of Mathematics, University of Maryland, 20742 College Park, MD, USA |
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Abstract: | We consider a compact invariant set of an expanding map of a manifoldM and give upper and lowerbounds for the Hausdorff Dimension dimH(), and box dimensionsdimB() and dimB(). 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.Part of this work was done when I was in the Department of Mathematics, University of Arizona. |
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