JournalsjemsVol. 24, No. 7pp. 2361–2441

Hausdorff dimension of planar self-affine sets and measures with overlaps

  • Michael Hochman

    The Hebrew University of Jerusalem, Israel; Institute for Advanced Study, Princeton, USA
  • Ariel Rapaport

    Cambridge University, UK; The Hebrew University of Jerusalem, Israel; Technion, Haifa, Israel
Hausdorff dimension of planar self-affine sets and measures with overlaps cover
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Abstract

We prove that if μ\mu is a self-affine measure in the plane whose defining IFS acts totally irreducibly on RP1\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 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. 2361–2441

DOI 10.4171/JEMS/1127