Invariant measures for substitutions on countable alphabets
Résumé
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 wellestablished 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.
Mots clés
substitutions on infinite alphabet unique ergodicity countable non-negative matrices shift dynamical systems )
37A25 37B10 37A50 (Secondary)
substitutions on infinite alphabet
unique ergodicity
countable non-negative matrices
shift dynamical systems )
37A25
37B10
37A50 (Secondary)
2020 Mathematics Subject Classification. 37A05 37A25 37B10 37A50 substitutions on infinite alphabet unique ergodicity countable nonnegative matrices shift dynamical systems
2020 Mathematics Subject Classification. 37A05
37A50 substitutions on infinite alphabet
countable nonnegative matrices
shift dynamical systems