The dimension of projections of planar diagonal self-affine measures

Authors

  • Aleksi Pyörälä University of Jyväskylä, Department of Mathematics and Statistics

Keywords:

Hausdorff dimension, orthogonal projections, self-affine measures

Abstract

We show that if \(\mu\) 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,
\(\operatorname{dim}_{\rm H} \mu \circ \pi^{-1} = \min \{ 1, \operatorname{dim}_{\rm H} \mu \}\)
for any non-principal orthogonal projection \(\pi\).
Section
Articles

Published

2025-02-07

How to Cite

Pyörälä, A. (2025). The dimension of projections of planar diagonal self-affine measures. Annales Fennici Mathematici, 50(1), 59–78. https://doi.org/10.54330/afm.156815