Work

Local mean dimension theory for sofic group actions

Year: 2025

Type: article

Abstract: Using a local perspective, we introduce mean dimension pairs and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group G has positive mean dimension. In addition, we show that the mean dimension map is Borel, and that the set of subshifts with completely positive mean dimension of [0,1]^{G} , the full G -shift on the interval, is a complete coanalytic set in the set of all subshifts (hence not Borel). Our results are new even when the acting group is \mathbb{Z} .

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/862

Authors: Felipe García-Ramos, Yonatan Gutman

Institutions: Jagiellonian University, Autonomous University of San Luis Potosí, Polish Academy of Sciences

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4409082043

FWCI: 1.636

Cites:

Cited by: 2

Related to: 10