The Hilbert cube contains a minimal subshift of full mean dimension
Volume 274 / 2024
Studia Mathematica 274 (2024), 1-10
MSC: Primary 37B99; Secondary 54F45.
DOI: 10.4064/sm210328-4-9
Published online: 27 November 2023
Abstract
We construct a minimal dynamical system of mean dimension $1$ which can be embedded in the shift action on the Hilbert cube $[0,1]^{\mathbb Z}$. This enables us to give the exact ranges of values of mean dimension for which there is a minimal dynamical system that can be (resp. cannot be) embedded in the shift action on the Hilbert cube.
