On the dimension of self-affine sets and measures with overlaps

Abstract

In this paper we consider diagonally affine, planar IFS $\Phi ={\left\{S_i(x,y)=({\alpha }_{i}x+t_{i,1},{\beta }_{i}y+t_{i,2})\right\}}_{i=1}^m$. Combining the techniques of Hochman and Feng, Hu we compute the Hausdorff dimension of the self-affine attractor and measures and we give an upper bound for the dimension of the exceptional set of parameters.

References in corpus (2)

• On self-similar sets with overlaps and inverse theorems for entropy in ${\mathbb{R}}^d$
• On the dimensions of a family of overlapping self-affine carpets