Substitution dynamical systems on infinite alphabets
[Substitutions sur un alphabet infini]
Ferenczi, Sébastien1
1 Institut de Mathématiques de Luminy CNRS, UPR 9016 163 av. de Luminy 13288 Marseille Cedex 9 (France) and Fédération de Recherche des Unités de Mathématiques de Marseille CNRS - FR 2291
Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2315-2343.

Nous étudions quelques exemples de substitutions sur des alphabets infinis, et jetons les bases d’une théorie générale des systèmes dynamiques associés. En particulier la substitution “de l’ivrogne” définit un système préservant une mesure infinie ergodique, d’entropie de Krengel nulle, tandis que les substitutions de longueur constante dont la matrice est positive récurrente correspondent à des systèmes préservant des mesures finies ergodiques.

We give a few examples of substitutions on infinite alphabets, and the beginning of a general theory of the associated dynamical systems. In particular, the “drunken man” substitution can be associated to an ergodic infinite measure preserving system, of Krengel entropy zero, while substitutions of constant length with a positive recurrent infinite matrix correspond to ergodic finite measure preserving systems.

DOI : 10.5802/aif.2242
Classification : 37A05, 37A40, 37B10
Keywords: Substitutions, dynamical systems
Mot clés : Substitutions, systèmes dynamiques
Ferenczi, Sébastien 1

1 Institut de Mathématiques de Luminy CNRS, UPR 9016 163 av. de Luminy 13288 Marseille Cedex 9 (France) and Fédération de Recherche des Unités de Mathématiques de Marseille CNRS - FR 2291 
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Ferenczi, Sébastien. Substitution dynamical systems on infinite alphabets. Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2315-2343. doi : 10.5802/aif.2242. https://www.numdam.org/articles/10.5802/aif.2242/

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