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Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps
Published 22 Apr 2019 in math.DS and math.MG | (1904.09812v2)
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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