Multifractal analysis for the pointwise Assouad dimension of self-similar measures
Dynamical Systems
2024-01-09 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2401.03953,
title = {Multifractal analysis for the pointwise Assouad dimension of self-similar measures},
author = {Roope Anttila and Ville Suomala},
journal= {arXiv preprint arXiv:2401.03953},
year = {2024}
}
Comments
22 pages, 1 figure. Comments are welcome!