English

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 11, which can be embedded in the shift action on the Hilbert cube [0,1]Z[0,1]^\mathbb{Z}. 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.

Keywords

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}
}