A modified multifractal formalism for a class of self-similar measures with overlap

Abstract

We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urba´nski [23]. We extend their results to the overlapping region and also consider some extensions and generalizations