The Hilbert cube contains a minimal subshift of full mean dimension
Dynamical Systems
2024-02-19 v4
Abstract
We construct a minimal dynamical system of mean dimension equal to , which can be embedded in the shift action on the Hilbert cube . This clarifies a seemingly plausible impression about embedding possibility in relation to mean dimension. Our result finally leads to a full understanding of a pair of exact ranges of all the possible values of mean dimension, within which there will always be a minimal dynamical system that can/cannot be embedded in the shift action on the Hilbert cube.
Cite
@article{arxiv.2102.10339,
title = {The Hilbert cube contains a minimal subshift of full mean dimension},
author = {Lei Jin and Yixiao Qiao},
journal= {arXiv preprint arXiv:2102.10339},
year = {2024}
}