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arXiv · 1904.09812

Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps

Michael Hochman·Ariel Rapaport
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Abstract

We prove that if $\mu$ is a self-affine measure in the plane whose defining IFS acts totally irreducibly on $\mathbb{RP}^1$ and satisfies an exponential separation condition, then its dimension is equal to its Lyapunov dimension. We also treat a class of reducible systems. This extends our previous work on the subject with B\'ar\'any to the overlapping case.

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Michael Hochman, Ariel Rapaport. 2019-04-22. Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps. https://arxiv.org/abs/1904.09812

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