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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Bibliographic Details
Published in:Advances in mathematical physics 2014-01, Vol.2014 (2014), p.1-8
Main Authors: Xiao, JiaQing, He, YouMing
Format: Article
Language:English
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Colleges & universities
Nonlinear systems
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Summary: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2014/161756