Comment.Math.Univ.Carolin. 50,2 (2009)221–243 221 Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations

Hofbauer Abstract. We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights using the recurrence time of a set and equilibrium states respectively