An extension of Minkowski's singular function
type: Item
instance of: scholarly article
title: An extension of Minkowski's singular function
zbMATH Open document ID: 0871.26008
DOI: 10.1016/0893-9659(95)00064-W
author: J. Uitz
author: Robert F. Tichy
published in: Applied Mathematics Letters
publication date: 1997-08-31T00:00:00Z
review text: The authors introduce a family of continuous strictly increasing singular (Cantor type) functions \(g_\lambda :[0,1]\rightarrow [0,1]\), \(\lambda \in (0,1)\). The Hausdorff dimension of the set of points where \(g_\lambda \) has a nonvanishing derivative is computed. For \(\lambda =1/2\) one obtains the Minkowski's singular function studied by J.R. Kinney.
Mathematics Subject Classification ID: 26A30
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 828422
zbMATH Keywords: Minkowski's singular function
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: Farey shift
zbMATH Keywords: chaotic systems
reviewed by: Valeriu Anisiu
MaRDI profile type: Publication
cites work: Note on a Singular Function of Minkowski
cites work: On the Definition of Chaos
cites work: Q4694260
cites work: Q4040797
cites work: Q3769642
cites work: The dimension of some sets defined in terms of f-expansions
cites work: On Some Singular Monotonic Functions Which Are Strictly Increasing
description: scientific article; zbMATH DE number 828422