Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps
Dynamical Systems
2019-05-06 v2 Metric Geometry
Abstract
We prove that if is a self-affine measure in the plane whose defining IFS acts totally irreducibly on 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.
Keywords
Cite
@article{arxiv.1904.09812,
title = {Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps},
author = {Michael Hochman and Ariel Rapaport},
journal= {arXiv preprint arXiv:1904.09812},
year = {2019}
}
Comments
84 pages. v2: Correction to statement of Thm 4.1 (requires uniform entropy dimension, now defined in Def 3.14), and adjusted quantifier order in proof of Cor. 4.2. No changes to main results