可数字母表上替换的不变度量

Pub Date : 2023-12-11 DOI:10.1017/etds.2023.113

WEBERTY DOMINGOS, SÉBASTIEN FERENCZI, ALI MESSAOUDI, GLAUCO VALLE

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引用次数: 0

摘要

在这项研究中，我们研究了与无限可数字母表上的替换相关联的符号动力系统的遍历和动力学特性。具体来说，我们考虑的是与不可还原替换相关的移位动力系统，它在有限字母表的情况下具有公认的性质。基于与置换相关的可数整数矩阵的动力学性质，我们得到了关于移位不变度量的存在性和唯一性的结果。

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Invariant measures for substitutions on countable alphabets

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.

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