A Class of Self-Similar Fractals with Overlap Structure
A Class of Self-Similar Fractals with Overlap Structure
复制标题
DOI：
10.1006/aama.1997.0560
复制
发表时间：
1998
影响因子：
1.1
通讯作者：
H. Rao;Z. Wen
中科院分区：
文献类型：
--
作者：
H. Rao;Z. Wen
对于压缩相似函数S_1(X)=x/3，S_2(X)=(x+？)/3，S_3(X)=(x+2)/3，其中？0，1表示关于TOS_1，S_2和S_3的不变集。本文研究了Hausdorff测度、Hausdorff维数和结构Off？设？=b/a？q？0，1，(a，b)=1.利用组合技巧，我们证明了|F？|0 IFA？B？0(Mod3)；否则，F？是一个具有递归结构的类Cantor分形.
For the contracting similaritiesS1(x)=x/3,S2(x)=(x+?)/3, andS3(x)=(x+2)/3, where ??0,1, letF?denote the invariant set with respect toS1,S2, andS3. In this paper, we study the Hausdorff measure, Hausdorff dimension, and the structure ofF?. Let ?=b/a?Q?0,1, (a,b)=1. Using combinatorial techniques, we show that |F?|0 ifa?b?0 (mod3); otherwise,F?is a Cantor-like fractal with recursive construction.