Transversality and beta-transformations

By making use of a transversality technique by Solomyak one can calculate the Hausdorff dimension of the attractor of some transformations similar to the baker's transformation, for almost all parameters with contraction less than about 0.64. I will talk about how to extend such results to contractions larger than 0.64, for some skew-products with beta-transformations. I will also make use of some results on so called derivable sequences, and their relation to natural extensions of beta-shifts.