TY - JOUR
T1 - Hausdorff dimension of planar self-affine sets and measures
AU - Bárány, Balázs
AU - Hochman, Michael
AU - Rapaport, Ariel
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85062704684&partnerID=8YFLogxK
U2 - 10.1007/s00222-018-00849-y
DO - 10.1007/s00222-018-00849-y
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AN - SCOPUS:85062704684
SN - 0020-9910
VL - 216
SP - 601
EP - 659
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -