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arXiv · 1504.07138

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

Balázs Bárány·Michał Rams·Károly Simon
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Abstract

In this paper we consider diagonally affine, planar IFS $\Phi=\left\{S_i(x,y)=(\alpha_ix+t_{i,1},\beta_iy+t_{i,2})\right\}_{i=1}^m$. 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.

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Balázs Bárány, Michał Rams, Károly Simon. 2015-04-27. On the dimension of self-affine sets and measures with overlaps. https://arxiv.org/abs/1504.07138

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