Remark on the local nature of metric mean dimension

Abstract

Metric mean dimension is a metric invariant of dynamical systems. It is a dynamical analogue of Minkowski dimension of metric spaces. We explain that old ideas of Bowen (1972) can be used for clarifying the local nature of metric mean dimension. We also explain the generalization to ${\mathbb{R}}^D$-actions and an illustrating example.

arXiv comment20 pages