Bertrand-Mathis, Anne; Volkmann, Bodo On \((\epsilon,k)\)-normal words in connecting dynamical systems. (English) Zbl 0648.10032 Monatsh. Math. 107, No. 4, 267-279 (1989). It was shown by A. Copeland and P. Erdős [Bull. Am. Math. Soc. 52, 857-860 (1946)] that a real number \(\alpha\) of the form \(\alpha =.a_ 1a_ 2...,\) obtained by catenating the base \(g\) (\(g\geq 2\); integer) digit blocks of a sequence \(a_ 1<a_ 2<..\). of integers, is normal if the \(a_ n\) satisfy a certain growth condition (example: primes). The authors generalize this result to infinite words obtained by catenating words from a language over a finite alphabet, satisfying a certain “connecting condition” (For any two words a, b there exists a word u of bounded length such that aub is a word). In particular, this leads to a generalization of the Copeland-Erdős Theorem to digit expansion with a Pisot number as base. Reviewer: B.Volkmann Cited in 2 ReviewsCited in 6 Documents MSC: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11K36 Well-distributed sequences and other variations 94A17 Measures of information, entropy Keywords:symbolic dynamical systems; entropy; infinite words; language; finite alphabet; Copeland-Erdős theorem; digit expansion; Pisot number PDFBibTeX XMLCite \textit{A. Bertrand-Mathis} and \textit{B. Volkmann}, Monatsh. Math. 107, No. 4, 267--279 (1989; Zbl 0648.10032) Full Text: DOI EuDML References: [1] Bertrand-Mathis, A.: Développements en base ?, répartion modulo un de la suitex ? n n?0,, langages codés et ?-shifts. Bull. Soc. Math. France114, 271-323 (1986). · Zbl 0628.58024 [2] Bertrand-Mathis, A.: Points génériques de Champernowne sur certains systèmes codés; applications aux ?-shifts. Ergodic Theory and Dynamical Systems8, 35-51 (1988). · Zbl 0657.28014 [3] Bertrand-Mathis, A.: Spécification et synchronisation. University of Bordeaux I: Preprint. [4] Bertrand-Mathis, A.: Comment écrire des nombres entiers dans une base qui n’est pas entière. Acta Math. Hung. To appear. · Zbl 1383.11009 [5] Besicovitch, A. S.: The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers. Math. Z.39, 146-156 (1935). · Zbl 0009.20002 [6] Billingsley, P.: Ergodic Theory and Information. New York: Wiley. 1965. · Zbl 0141.16702 [7] Blanchard, F., Hansel, G.: Systèmes codés. Theoretical Computer Science44, 17-49 (1986). · Zbl 0601.68056 [8] Champernowne, D.: The construction of decimals normal in the scale of ten. J. London Math. Soc.8, 254-260 (1933). · Zbl 0007.33701 [9] Copeland, A., Erdös, P.: Note on normal numbers. Bull. Amer. Math. Soc.52, 857-860 (1946). · Zbl 0063.00962 [10] Denker, M., Grillenberger, C., Sigmund, K.: Ergodic Theory on Compact Spaces. Lect. Notes Math.527. Berlin-Heidelberg-New York: Springer 1976. · Zbl 0328.28008 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.