Work

Naive mean dimension

Year: 2025

Type: article

Abstract: We investigate the dynamical property of the naive mean dimension for continuous actions of any countable group on compact metrizable spaces. It is shown that naive mean dimension serves as an upper bound of sofic mean dimension for actions of nonamenable groups. For algebraic actions we obtain more satisfactory results by looking at the naive version of mean rank for modules over integral group rings. We also consider the naive metric mean dimension and investigate its relations with sofic metric mean dimension.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2025050

Authors: Bingbing Liang, Kesong Yan

Institution: Soochow University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Awards: G1443926617, G3976637566