Hausdorff dimension of planar self-affine sets and measures

Balázs Bárány, Michael Hochman, Ariel Rapaport

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


Let X =ϕi X be a strongly separated self-affine set in R2 (or one satisfying the strong open set condition). Under mild non-conformality and irreducibility assumptions on the matrix parts of the ϕi, we prove that dim X is equal to the affinity dimension, and similarly for self-affine measures and the Lyapunov dimension. The proof is via analysis of the dimension of the orthogonal projections of the measures, and relies on additive combinatorics methods.

Original languageAmerican English
Pages (from-to)601-659
Number of pages59
JournalInventiones Mathematicae
Issue number3
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.


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