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

Bárány, Balázs; MichałRams; Simon, Károly

doi:10.1090/proc/13121

On the dimension of self-affine sets and measures with overlaps
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by Balázs Bárány, MichałRams and Károly Simon PDF

Proc. Amer. Math. Soc. 144 (2016), 4427-4440 Request permission

Abstract:

In this paper we consider diagonally affine, planar IFS $\Phi =$ $\{S_i(x,y)\!=\!(\alpha _ix+t_{i,1},\beta _iy+t_{i,2})\}_{i=1}^m$. Combining the techniques of Hochman and Feng and 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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