On the distribution of digits in dyadic expansions
type: Item
instance of: scholarly article
title: On the distribution of digits in dyadic expansions
zbMATH Open document ID: 0909.28004
DOI: 10.1007/BF03322068
author: D. Massart
published in: Results in Mathematics
publication date: 1999-03-22T00:00:00Z
review text: This paper provides a precise estimate of the Hausdorff dimension of the following set \[ \Biggl\{x\in [0,1]: \lim_{N\to\infty} {1\over N} \sum^N_{n= 1} \prod^r_{k= 0} \varepsilon_{n+k}(x)= q\Biggr\}, \] where the digits \(\varepsilon_n(x)\in \{0,1\}\) are the digits of the dyadic expansion of \(x\), \(q\in [0,1]\) and \(r= 2,3,4\dots\)\ . The proof involves the construction of Markov measures. The paper ends with a multifractal analysis of these measures.
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 28D99
zbMATH DE Number: 1140104
zbMATH Keywords: multifractal analysis
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: dyadic expansion
zbMATH Keywords: Markov measures
reviewed by: Valérie Berthé
MaRDI profile type: Publication
cites work: On the sum of digits of real numbers represented in the dyadic system. (On sets of fractional dimensions II.)
cites work: Q5515914
cites work: Q4291229
cites work: Dimension and entropy of a non-ergodic Markovian process and its relation to Rademacher Riesz products
cites work: Hausdorff dimension and Perron-Frobenius theory
cites work: Sets of Fractional Dimensions which Occur in Some Problems of Number Theory
cites work: Sur les dimensions de mesures
cites work: Q4722916
cites work: Q4694303
cites work: Dyadic expansions and Hausdorff measure
cites work: Über Hausdorffsche Dimensionen von Mengen, die durch Zifferneigenschaften charakterisiert sind. I
full work available at URL: https://doi.org/10.1007/bf03322068
OpenAlex ID: W2110233935
description: scientific article; zbMATH DE number 1140104