Hausdorff dimension of attractors for two dimensional Lorenz transformations

A class of transformations on [0, 1](2), which includes transformations obt ained by a Poincare section of the Lorenz equation, is considered. We prove that the Hausdorff dimension of the attractor of these transformations equ als z + 1 where z is the unique zero of a certain pressure function. Furthe rmore we prove that all vertical intersections with this attractor, except of countable many, have Hausdorff dimension z.