Dimensions of invariant sets of expanding maps

We consider a compact invariant set of an expanding map of a manifoldM and give upper and lowerbounds for the Hausdorff Dimension dim _H (), and box dimensionsdim _B () and dim _B (). 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.