Trees with non-regular fractal boundary

被引：0
|
作者：
Jing Hu Yu
Yi Ming Ding
机构：
[1] Wuhan University of Technology,Department of Mathematics, School of Sciences
[2] Chinese Academy of Sciences,Wuhan Institute of Physics and Mathematics
来源：
Acta Mathematica Sinica, English Series | 2008年 / 24卷
关键词：
tree; boundary; fractal; dimensions; non-regularity; recursive structures; 60G17; 60J80;
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学科分类号：
摘要：
For any given 0 < α < β < ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, nonregular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.
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