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

Balázs Bárány; Michał Rams; Károly Simon

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

Dynamical Systems 2015-12-24 v2

Authors: Balázs Bárány , Michał Rams , Károly Simon

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.

Keywords

self-affine sets self-affine measures Hausdorff dimension iterated function systems overlaps planar IFS exceptional parameters

Cite

@article{arxiv.1504.07138,
  title  = {On the dimension of self-affine sets and measures with overlaps},
  author = {Balázs Bárány and Michał Rams and Károly Simon},
  journal= {arXiv preprint arXiv:1504.07138},
  year   = {2015}
}

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