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… (More)
We consider completely invariant subsets A of weakly expanding piece-wise monotonic transformations T on 0;1]. It is shown that the upper box dimension of A is bounded by the minimum t A of all parameters t for which a t-conformal measure with support A exists. In particular, this implies equality of box dimension and Hausdorr dimension of A.