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arXiv · 2308.11399

Scaling limits of self-conformal measures

Balázs Bárány·Antti Käenmäki·Aleksi Pyörälä·Meng Wu
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Abstract

We show that any self-conformal measure $\mu$ on $\mathbb{R}$ is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the need for any separation condition. We also obtain applications to the prevalence of normal numbers in self-conformal sets, the resonance between self-conformal measures on the line, and projections of self-affine measures on carpets.

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Balázs Bárány, Antti Käenmäki, Aleksi Pyörälä, Meng Wu. 2023-08-22. Scaling limits of self-conformal measures. https://arxiv.org/abs/2308.11399

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