Mean dimension of continuous cellular automata
Dynamical Systems
2021-05-21 v1
Abstract
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, a CA permutative algebraic or having a spaceship has infinite mean dimension. However, building on Meyerovitch's example, we give an example of algebraic surjective cellular automaton with positive finite mean dimension.
Keywords
Cite
@article{arxiv.2105.09708,
title = {Mean dimension of continuous cellular automata},
author = {David Burguet and Ruxi Shi},
journal= {arXiv preprint arXiv:2105.09708},
year = {2021}
}
Comments
21 pages