Lipschitz equivalence of fractal sets in R  

作　　者：DENG GuoTai HE XingGang 

机构地区：[1]College of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China

出　　处：《Science China Mathematics》2012年第10期2095-2107,共13页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871180)

摘　　要：Let T（q, D） be a self-similar （fractal） set generated by {fi（x） = 1/q（（x ＋ di）}^Ni=1 where integer q 〉 1and D = {d1, d2 dN} C R. To show the Lipschitz equivalence of T（q, D） and a dust-iik-e T（q, C）, one general restriction is 79 C Q by Peres et al. [Israel] Math, 2000, 117： 353-379]. In this paper, we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques. Several examples are given to illustrate our theory.Let T(q,D) be a self-similar(fractal) set generated by {fi(x) = 1 q(x + di)}iN=1 where integer q > 1 and D = {d1,d2,...,dN } R.To show the Lipschitz equivalence of T(q,D) and a dust-like T(q,C),one general restriction is D Q by Peres et al.[Israel J Math,2000,117:353-379].In this paper,we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques.Several examples are given to illustrate our theory.

关 键 词：dust-like graph-directed iterating function systems Lipschitz equivalence self-similar sets 

分 类 号：O174.41[理学—数学] O171[理学—基础数学]