Invariant measures for substitutions on countable alphabets

Author(s)

Domingos, Weberty ; Ferenczi, Sebastien ; Messaoudi, Ali ; Valle, Glauco

• Document type: Journal article
• Source: Ergodic Theory and Dynamical Systems; v. 44, n. 9, p. 32-pg., 2023-12-11.

Abstract

In this work, we study ergodic and dynamical properties of symbolic dynamical system associated to substitutions on an infinite countable alphabet. Specifically, we consider shift dynamical systems associated to irreducible substitutions which have well-established properties in the case of finite alphabets. Based on dynamical properties of a countable integer matrix related to the substitution, we obtain results on existence and uniqueness of shift invariant measures. (AU)

• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants