THE HAUSDORFF DIMENSION OF SELF-SIMILAR SETS UNDER A PINCHING CONDITION

We study self-similar sets in the case where the construction diffeomorphisms are not necessarily conformal. Using topological pressure we give an upper estimate of the Hausdorff dimension, when the construction diffeomorphisms are C1+K and satisfy a K-pinching condition for some K less-than-or-equal-to 1 . Moreover, if the construction diffeomorphisms also satisfy the disjoint open set condition we then give a lower bound for the Hausdorff dimension.