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

Michael Hochman, Ariel Rapaport

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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

Original languageAmerican English
Pages (from-to)2361-2441
Number of pages81
JournalJournal of the European Mathematical Society
Issue number7
StatePublished - 2022

Bibliographical note

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  • Hausdorff dimension
  • Lyapunov dimension
  • self-affine measure
  • self-affine set


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