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arXiv · 1503.01270

Planar self-affine sets with equal Hausdorff, box and affinity dimensions

Kenneth Falconer·Tom Kempton
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Abstract

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.

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Kenneth Falconer, Tom Kempton. 2015-03-04. Planar self-affine sets with equal Hausdorff, box and affinity dimensions. https://arxiv.org/abs/1503.01270

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