| Consider a compact invariant set of a differentiable dynamical system. The Hausdorff dimension of such a set is closely related to the dynamical behavior of the map defining the system. This thesis studies systems with strict expanding property, which include the finite-dimensional and infinite-dimensional expanding maps and the hyperbolic sets. We focus on non-conformal systems. Various upper and lower bounds for the Hausdorff dimension are provided. The major upper bound is constructed using the expanding ratios and the topological pressure, which generalizes a formula of R. Bowen and D. Ruelle on conformal maps. For some well-known invariant sets the bound has the property that it exactly equals the dimension in typical cases. Other bounds are also obtained by means of topological entropy, measure-theoretical entropy and Lyapunov exponents. These bounds have improved or supplemented current results. |
