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<p>The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting.</p>

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Local dimension spectrum for dominated planar self-affine sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月24日

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  • Alex Batsis,
  • Antti Käenmäki,
  • Tom Kempton

摘要

The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting.