Lipschitz equivalence of fractal sets in R
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,...
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| Veröffentlicht in: | Science China. Mathematics 2012-10, Vol.55 (10), p.2095-2107 |
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| container_title | Science China. Mathematics |
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| creator | Deng, GuoTai He, XingGang |
| description | 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. |
| doi_str_mv | 10.1007/s11425-012-4444-5 |
| format | Article |
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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. 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| subjects | Applications of Mathematics Astronomy China Combinatorial analysis Constrictions Criteria Equivalence Fractal analysis Fractals Functions (mathematics) Lipschitz Mathematical analysis Mathematics Mathematics and Statistics Self-similarity 以色列 分形集 技术使用 等价 自相似集 迭代函数系统 |
| title | Lipschitz equivalence of fractal sets in R |
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