Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures

The point x for which the limit limr→0⁡(log⁡μBx,r/log⁡r) does not exist is called divergence point. Recently, multifractal structure of the divergence points of self-similar measures has been investigated by many authors. This paper is devoted to the study of some Moran measures with the support on...

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Main Authors: JiaQing Xiao, YouMing He
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2014/161756
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author JiaQing Xiao
YouMing He
author_facet JiaQing Xiao
YouMing He
author_sort JiaQing Xiao
collection DOAJ
description The point x for which the limit limr→0⁡(log⁡μBx,r/log⁡r) does not exist is called divergence point. Recently, multifractal structure of the divergence points of self-similar measures has been investigated by many authors. This paper is devoted to the study of some Moran measures with the support on the homogeneous Moran fractals associated with the sequences of which the frequency of the letter exists; the Moran measures associated with this kind of structure are neither Gibbs nor self-similar and than complex. Such measures possess singular features because of the existence of so-called divergence points. By the box-counting principle, we analyze multifractal structure of the divergence points of some homogeneous Moran measures and show that the Hausdorff dimension of the set of divergence points is the same as the dimension of the whole Moran set.
format Article
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institution Kabale University
issn 1687-9120
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language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Advances in Mathematical Physics
spelling doaj-art-8867fc97ce85482dac87296cbb765fd82025-08-20T03:38:06ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/161756161756Multifractal Structure of the Divergence Points of Some Homogeneous Moran MeasuresJiaQing Xiao0YouMing He1Wuhan College, Zhongnan University of Economics and Law, Wuhan 430070, ChinaWuhan College, Zhongnan University of Economics and Law, Wuhan 430070, ChinaThe point x for which the limit limr→0⁡(log⁡μBx,r/log⁡r) does not exist is called divergence point. Recently, multifractal structure of the divergence points of self-similar measures has been investigated by many authors. This paper is devoted to the study of some Moran measures with the support on the homogeneous Moran fractals associated with the sequences of which the frequency of the letter exists; the Moran measures associated with this kind of structure are neither Gibbs nor self-similar and than complex. Such measures possess singular features because of the existence of so-called divergence points. By the box-counting principle, we analyze multifractal structure of the divergence points of some homogeneous Moran measures and show that the Hausdorff dimension of the set of divergence points is the same as the dimension of the whole Moran set.http://dx.doi.org/10.1155/2014/161756
spellingShingle JiaQing Xiao
YouMing He
Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
Advances in Mathematical Physics
title Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
title_full Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
title_fullStr Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
title_full_unstemmed Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
title_short Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
title_sort multifractal structure of the divergence points of some homogeneous moran measures
url http://dx.doi.org/10.1155/2014/161756
work_keys_str_mv AT jiaqingxiao multifractalstructureofthedivergencepointsofsomehomogeneousmoranmeasures
AT youminghe multifractalstructureofthedivergencepointsofsomehomogeneousmoranmeasures