Divergence points of self-similar measures satisfying the OSC |
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Authors: | Jia-Qing Xiao Min Wu |
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Institution: | a School of Science, Wuhan University of Technology, Wuhan 430070, China b Department of Mathematics, South China University of Technology, Guangzhou 510640, China |
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Abstract: | Recently, Barreira and Schmeling (2000) 1] and Chen and Xiong (1999) 2] have shown, that for self-similar measures satisfying the SSC the set of divergence points typically has the same Hausdorff dimension as the support K. It is natural to ask whether we obtain a similar result for self-similar measures satisfying the OSC. However, with only the OSC satisfied, we cannot do most of the work on a symbolic space and then transfer the results to the subsets of Rd, which makes things more difficult. In this paper, by the box-counting principle we show that the set of divergence points has still the same Hausdorff dimension as the support K for self-similar measures satisfying the OSC. |
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Keywords: | Divergence point Open set condition _method=retrieve& _eid=1-s2 0-S0022247X11001272& _mathId=si2 gif& _pii=S0022247X11001272& _issn=0022247X& _acct=C000053510& _version=1& _userid=1524097& md5=fa6880fc1ba44114bc30fb3654300e88')" style="cursor:pointer Lq-spectra" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">Lq-spectra |
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