Mean dimension theory in symbolic dynamics for finitely generated amenable groups
Dynamical Systems
2021-03-30 v1
Abstract
In this paper, we mainly elucidate a close relationship between the topological entropy and mean dimension theory for actions of polynomial growth groups. We show that metric mean dimension and mean Hausdorff dimension of subshifts with respect to the lower rank subgroup are equal to its topological entropy multiplied by the growth rate of the subgroup. Meanwhile, we also prove the above result holds for the rate distortion dimension of subshifts with respect to the lower rank subgroup and measure entropy. Furthermore, some relevant examples are indicated.
Cite
@article{arxiv.2103.14817,
title = {Mean dimension theory in symbolic dynamics for finitely generated amenable groups},
author = {Yunping Wang and Ercai Chen and Xiaoyao Zhou},
journal= {arXiv preprint arXiv:2103.14817},
year = {2021}
}