The singularity spectrum for general Sierpiński carpets
type: Item
instance of: scholarly article
title: The singularity spectrum for general Sierpiński carpets
zbMATH Open document ID: 0845.28007
author: James F. King
published in: Advances in Mathematics
publication date: 1996-09-11T00:00:00Z
review text: This paper is devoted to the study of the singularity spectrum of a class of two-dimensional Borel probability measures defined on general Sierpiński carpets, satisfying some disjointness condition (the singularity spectrum measures the variations of the local dimension of a measure). Even if Sierpiński carpets have a particular behaviour with respect to the one-dimensional case, the usual properties of the one-dimensional known examples of singularity spectrum are found here: the singularity spectrum is a smooth concave down function with a single critical point and is numerically computable as a Legendre transform.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 838703
zbMATH Keywords: iterated function system
zbMATH Keywords: IFS
zbMATH Keywords: singularity spectrum
zbMATH Keywords: Sierpiński carpets
reviewed by: Valérie Berthé
MaRDI profile type: Publication
full work available at URL: aima.1995.1061
OpenAlex ID: W2090541396
DOI: 10.1006/AIMA.1995.1061
description: scientific article; zbMATH DE number 838703