Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals
Dynamical Systems
2026-01-05 v1 Classical Analysis and ODEs
Abstract
We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Assouad spectrum. This provides a new family of bi-Lipschitz invariants of dynamical systems. We study its basic properties and calculate it for several classes of dynamical systems. As an application, we determine explicit formulae for the mean Assouad dimension and spectrum of infinite-dimensional Bedford--McMullen carpet systems, contributing to the program of studying infinite dimensional fractals, initiated recently by Tsukamoto.
Keywords
Cite
@article{arxiv.2601.00233,
title = {Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals},
author = {Qiang Huo and Adam Śpiewak},
journal= {arXiv preprint arXiv:2601.00233},
year = {2026}
}
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32 pages