Work

Homomorphisms from aperiodic subshifts to subshifts with the finite extension property

Year: 2025

Type: article

Abstract: Given a countable group G and two subshifts X and Y over G , a continuous, shift-commuting map $\phi : X \to Y$ is called a homomorphism. Our main result states that if G is locally virtually nilpotent, X is aperiodic, and Y has the finite extension property, then there exists a homomorphism $\phi : X \to Y$ . By combining this theorem with the main result of [1], we obtain that if the same conditions hold, and if additionally the topological entropy of X is less than the topological entropy of Y and Y has no global period, then X embeds into Y .

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.16

Authors: ROBERT BLAND, KEVIN MCGOFF

Institution: University of North Carolina at Charlotte

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Division of Mathematical Sciences