Planar self-affine sets with equal Hausdorff, box and affinity dimensions

Abstract

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.

arXiv comment18 pages, 2 figures