Ferenczi, Sébastien Substitution dynamical systems on infinite alphabets. (English. French summary) Zbl 1147.37007 Ann. Inst. Fourier 56, No. 7, 2315-2343 (2006). Summary: 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. Cited in 16 Documents MSC: 37B10 Symbolic dynamics 37A05 Dynamical aspects of measure-preserving transformations 37A40 Nonsingular (and infinite-measure preserving) transformations Keywords:measure-preserving system PDFBibTeX XMLCite \textit{S. Ferenczi}, Ann. Inst. Fourier 56, No. 7, 2315--2343 (2006; Zbl 1147.37007) Full Text: DOI Numdam Numdam EuDML References: [1] CASSAIGNE, J., Complexité et facteurs spéciaux. Complexity and special factor, Bull. Belg. Math. Soc. Simon Stevin, 4, 4, 1, 67-88 (1997) · Zbl 0921.68065 [2] DURAND, F., A characterization of substitutive sequences using return words, Discrete Math., 179, 89-101 (1998) · Zbl 0895.68087 [3] FERENCZI, S., Complexity of sequences and dynamical systems, Discrete Math., 206, 145-154 (1999) · Zbl 0936.37008 [4] HOPF, E., Ergodentheorie (1937) · Zbl 0185.29001 [5] KITCHENS, B., Symbolic dynamics. One-sided, two-sided and countable state Markov shifts (1998) · Zbl 0892.58020 [6] KRENGEL, U., Entropy of conservative transformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 7, 161-181 (1967) · Zbl 0183.19303 [7] LE GONIDEC, M., Sur la complexité de mots infinis engandrés par des \(q\)-automates dénombrables · Zbl 1121.68090 [8] MAUDUIT, C., Propriétés arithmétiques des substitutions et automates infinis · Zbl 1147.11016 [9] MOSSÉ, B., Puissances de mots et reconnaissabilité des points fixes d’une substitution, Theoret. Comput. Sci., 99, 2, 327-334 (1992) · Zbl 0763.68049 [10] PYTHEAS FOGG, N., The universal counter-example [11] PYTHEAS FOGG, N., Lecture Notes in Math., 1794 (2002) · Zbl 1014.11015 [12] QUEFFÉLEC, M., Lecture Notes in Math., 1294 (1987) · Zbl 0642.28013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.