Hausdorff dimension of planar self-affine sets and measures
成果类型：
Article
署名作者：
Barany, Balazs; Hochman, Michael; Rapaport, Ariel
署名单位：
MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; Hebrew University of Jerusalem
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-00849-y
发表日期：
2019
页码：
601-659
关键词：
摘要：
Let X=?phi iX 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 phi i, we prove that dimX 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.
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