Multifractal Structure of the Divergence Points of Some Homogeneous Moran Measures
The point x for which the limit limr→0(logμBx,r/logr) 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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| Language: | English |
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Wiley
2014-01-01
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| 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(logμBx,r/logr) 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 |
| id | doaj-art-8867fc97ce85482dac87296cbb765fd8 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| 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(logμBx,r/logr) 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 |