Work

A New Notion of Dimension for Dynamical Systems and Shift Embeddability

Year: 2026

Type: article

Abstract: A dynamical system $(X,T)$ ( X , T ) is shift embeddable if $(X,T)$ ( X , T ) embeds continuously and equivariantly in the shift over $[0,1]^{d}$ [ 0 , 1 ] d for some finite $d$ d . Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov’s mean dimension and Lebesgue covering dimension of finite orbits are not the only obstructions for shift embeddability. We present a new notion of dimension for dynamical systems over any countable group. We show that this new notion of dimension accounts for all known obstructions for shift embeddability.

Source: Geometric and Functional Analysis

DOI: 10.1007/s00039-026-00742-4

Author: Tom Meyerovitch

Institution: Ben-Gurion University of the Negev

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,390

Funder: Ben-Gurion University of the Negev