Multifractal formalism for self-similar functions under the action of nonlinear dynamical systems
type: Item
instance of: scholarly article
title: Multifractal formalism for self-similar functions under the action of nonlinear dynamical systems
zbMATH Open document ID: 0928.28002
published in: Constructive Approximation
publication date: 2000-01-02T00:00:00Z
review text: Multifractal formalism for self-similar functions associated to contractive similitudes has been established by \textit{S. Jaffard} [SIAM J. Math. Anal. 28, No. 4, 944-970 (1997; Zbl 0876.42021); ibid. 971-998 (1997; Zbl 0876.42022)]. In this paper, self-similar functions associated to some nonlinear contractions are studied. In particular, the author calculates the Hölder exponents \(\alpha(x)\) of such functions at any point \(x\), the spectrum of singularities and the Besov ``smoothness'' index and proves the multifractal formalism.
reviewed by: Y. Xiao
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 26A30
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B30
zbMATH DE Number: 1289871
zbMATH Keywords: Hölder exponent
zbMATH Keywords: Besov's ``smoothness'' index
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: spectrum of singularity
zbMATH Keywords: wavelet
zbMATH Keywords: multifractal formalism
zbMATH Keywords: nonlinear self-similar function
author: Mourad Ben Slimane
MaRDI profile type: Publication
full work available at URL: s003659900105
OpenAlex ID: W2138865513
DOI: 10.1007/S003659900105
description: scientific article; zbMATH DE number 1289871