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arXiv · 2410.03401

The dimension of projections of planar diagonal self-affine measures

Aleksi Pyörälä
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Abstract

We show that if $μ$ is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts, $$ \dim_{\rm H} μ\circ π^{-1}= \min\lbrace 1,\dim_{\rm H}μ\rbrace $$ for any non-principal orthogonal projection $π$.

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Aleksi Pyörälä. 2025-02-05. The dimension of projections of planar diagonal self-affine measures. https://arxiv.org/abs/2410.03401

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