Mean dimension for free semigroup actions. (English) Zbl 1484.37038
Summary: We consider finitely generated free semigroup actions on a compact metric space and generalize mean dimension, Lindenstrauss’ metric mean dimension for free semigroup actions. We give a Bufetov formula for metric mean dimension of free semigroup action. We also show the relationship between mean topological dimension and metric mean dimension.
MSC:
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
| 37C45 | Dimension theory of smooth dynamical systems |
