Mean dimension of natural extension of algebraic systems
Dynamical Systems
2023-08-15 v3
Abstract
Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of an algebraic cellular automaton coincides withthe mean dimension of its natural extension, which strengthens a result of Burguet and Shi \cite{BS21} with a different proof.
Keywords
Cite
@article{arxiv.2203.01122,
title = {Mean dimension of natural extension of algebraic systems},
author = {Bingbing Liang and Ruxi Shi},
journal= {arXiv preprint arXiv:2203.01122},
year = {2023}
}
Comments
11pages. Some typos are fixed. to be published