Divergence points of self-similar measures satisfying the OSC☆
Divergence points of self-similar measures satisfying the OSC☆
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DOI：
10.1016/j.jmaa.2011.02.015
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发表时间：
2011-07
影响因子：
1.3
通讯作者：
JiaQing Xiao;Min Wu;Fei Gao
中科院分区：
文献类型：
--
作者：
JiaQing Xiao;Min Wu;Fei Gao
最近，Barreira和Schmeling（2000）[1]以及Chen和Xiong（1999）[2]证明了，对于满足SSC的自相似测度，发散点集通常具有与支撑K相同的Hausdorff维数。这是自然的问，我们是否得到了类似的结果，自相似措施满足OSC。然而，只有OSC满足，我们不能在符号空间上完成大部分工作，然后将结果转移到Rd的子集上，这使得事情变得更加困难。本文利用计盒原理证明了满足OSC的自相似测度的发散点集仍具有与支撑K相同的Hausdorff维数。
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.