Hausdorff and packing dimensions of non-normal tuples of numbers: non-linearity and divergence points
type: Item
instance of: scholarly article
title: Hausdorff and packing dimensions of non-normal tuples of numbers: non-linearity and divergence points
zbMATH Open document ID: 1185.28015
author: L. Olsen
published in: Bulletin des Sciences Mathématiques
publication date: 2010-02-09T00:00:00Z
review text: Using some previous results of the author [\textit{L.Olsen}, J. Math. Pures Appl., IX. Sér. 82, No. 12, 1591--1649 (2003; Zbl 1035.37025); Aequationes Math. 71, No. 1-2, 29--53 (2006; Zbl 1089.37021); Bull. Sci. Math. 132, No. 8, 650--678 (2008; Zbl 1167.37021)]; [\textit{L. Olsen, S. Winter}, Bull. Sci. Math. 131, No. 6, 518--558 (2007; Zbl 1121.37024)], in the paper under review, the author discusses the sets of d-tuples of numbers defined in terms of the asymptotic behaviour of the frequencies of strings of digits in their \(N\)-adic expansion, and he gives a detailed account of the Hausdorff and packing dimensions for this kind of sets.
reviewed by: Hua Su
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 5667915
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: packing dimension
zbMATH Keywords: normal numbers
zbMATH Keywords: non-normal numbers
zbMATH Keywords: frequencies of digits
MaRDI profile type: Publication
full work available at URL: j.bulsci.2008.12.002
OpenAlex ID: W1983149725
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DOI: 10.1016/J.BULSCI.2008.12.002
description: scientific article; zbMATH DE number 5667915