Title: Overlapping self-affine sets

Authors: Pablo Shmerkin

Issue: Volume 55 (2006), Issue 4, 1291-1332

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 [Feliks Przytycki, Mariusz Urba\'nski, \textit{On the Hausdorff dimension of some fractal sets}, Studia Math. \textbf{93} (1989), 155--186]. We extend their results to the overlapping region and also consider some extensions and generalizations.