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arXiv · 2401.13626

Local dimension spectrum for dominated planar self-affine sets

Alex Batsis·Antti Käenmäki·Tom Kempton
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Abstract

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.

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Alex Batsis, Antti Käenmäki, Tom Kempton. 2024-01-24. Local dimension spectrum for dominated planar self-affine sets. https://arxiv.org/abs/2401.13626

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