| 熊瑛;奚李峰.满足开集条件的自相似集的Lipschitz等价[J].数学年刊A辑,2012,33(1):1~0 |
| 满足开集条件的自相似集的Lipschitz等价 |
| Lipschitz Equivalence of Self-similar Sets Satisfying the Open Set Condition |
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| DOI： |
| 中文关键词: Lipschitz 等价, 自相似集, 开集条件 |
| 英文关键词:Lipschitz equivalence, Self-similar set, Open set condition |
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| 中文摘要: |
| 固定 $r\in (0,1)$ 及整数 $N\geq 2$, 设 $E$ 和 $E'$ 为由 $N$ 个形如 $S(x)=\pm rx+b$ 的压缩映射所生成的自相似集. 设开集条件对于 $E$ 及 $E'$ 成立,并且所对应的开集为开区间, 证明了 $E$ 和 $E'$ Lipschitz 等价. |
| 英文摘要: |
| Fix r ∈ (0, 1) and an integer N > 2. Let E and E′ be self-similar sets generatedby N contraction mappings of the form S(x) = ±rx + b. Suppose that open set conditionshold for E and E′, where the corresponding open sets are open intervals, then E and E′ areLipschitz equivalent. |
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