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Scaling limits of self-conformal measures

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arxiv 2308.11399 v1 pith:4H2C3DFT submitted 2023-08-22 math.DS math.CA

classification math.DSmath.CA
keywords self-conformalmeasuresscalingapplicationscarpetsconditiondistributionergodic
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Smooth projections of self-similar measures

    math.DS 2026-07 accept novelty 8.0 of 10

    A spectral-gap criterion gives Sobolev regularity for prescribed projections of self-similar measures and yields explicit examples such as singular measures with all line projections smooth.

  2. Projections of self-affine sets onto lines

    math.CA 2026-07 accept novelty 8.0 of 10

    Under strong pinching and strong irreducibility of the linear parts, every line projection of a self-affine set attains the expected dimension; in the plane, strong irreducibility alone suffices.

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