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 Bárány to the overlapping case.
Cite this article
Michael Hochman, Ariel Rapaport, Hausdorff dimension of planar self-affine sets and measures with overlaps. J. Eur. Math. Soc. 24 (2022), no. 7, pp. 2361–2441DOI 10.4171/JEMS/1127