3 papers
math.DS2026
Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals
Qiang Huo, Adam Åpiewak
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 Ass…
math.DS2026
On the representation of measurable and continuous dynamical systems by Lipschitz functions
Yonatan Gutman, Qiang Huo
Two representations theorems are presented: 1. Any Borel action of a second countable locally compact group on a standard Borel space admits an injective -equivariant Bo…
math.DS2025
A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem
Yonatan Gutman, Qiang Huo, Masaki Tsukamoto
We prove that a continuous action of on a compact metrizable space equivariantly embeds into the shift action on the space of one-Lipschitz functions from $\mathbb{R…