Local dimension spectrum for dominated planar self-affine sets
Dynamical Systems
2026-01-21 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2401.13626,
title = {Local dimension spectrum for dominated planar self-affine sets},
author = {Alex Batsis and Antti Käenmäki and Tom Kempton},
journal= {arXiv preprint arXiv:2401.13626},
year = {2026}
}
Comments
39 pages