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arXiv · 2401.03953

Multifractal analysis for the pointwise Assouad dimension of self-similar measures

Roope Anttila·Ville Suomala
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Abstract

We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension.

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Roope Anttila, Ville Suomala. 2024-01-08. Multifractal analysis for the pointwise Assouad dimension of self-similar measures. https://arxiv.org/abs/2401.03953

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