Discrete Lyapunov exponents and Hansdorff dimension

We study certain metrics on subshifts of finite type for which we define th e discrete analogs of Lyapunov exponents. We prove Young's formula for mu-H ausdorff dimension. We give sufficient conditions on the above metrics for which the Hausdorff dimension is given by thermodynamic formalism. We apply these results to the Hausdorff dimension of the limit sets of geometricall y finite, purely loxodromic, Kleinian groups.