Dimension of homogeneous rational self-similar measures with overlaps
type: Item
instance of: scholarly article
title: Dimension of homogeneous rational self-similar measures with overlaps
zbMATH Open document ID: 1172.28003
author: Víctor Ruiz
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-04-29T00:00:00Z
review text: The self-similar measures play an important role in the studies of fractal geometry, the case having overlaps is still a difficult question. The author consider a class of self-similar measures with overlaps which are obtained from systems of homotheties with centres in a lattice where the contraction ratios are all equal to the inverse of a natural number \(L\). In this case, the author gets the local dimension of the measure as the Shannon entropy (up to a constant), which shows also some relations with the properties of the absolute continuity or singularity of the measure.
reviewed by: Hua Su
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 82D20
zbMATH DE Number: 5549434
zbMATH Keywords: self-similar measures
zbMATH Keywords: overlapping
zbMATH Keywords: dimension
zbMATH Keywords: Shannon entropy
zbMATH Keywords: ergodicity
zbMATH Keywords: hidden Markov chain
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.008
OpenAlex ID: W2035081222
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DOI: 10.1016/J.JMAA.2008.12.008
description: scientific article; zbMATH DE number 5549434