| 刘春苔.满足递推式紧集的 Lipschitz 等价性[J].数学年刊A辑,2013,34(6):643~652 |
| 满足递推式紧集的 Lipschitz 等价性 |
| Lipschitz Equivalence of Compact Sets with a Recurrence Equation |
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| DOI： |
| 中文关键词: 递推式, 自相似集, Lipschitz 等价 |
| 英文关键词:Recurrence equation, Self-similar set, Lipschitz equivalence |
| 基金项目:国家自然科学基金 (No.11271148), 中央高校基本科研业务费(No.CCNU11A01028) 和湖北省教育厅科学研究计划项目(No.B2013221) |
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| 中文摘要: |
| 设紧集$U$满足一个不交并递推式: $U=(rU+\Theta)\cup U_1$. 证明了若$U_1$与一个满足强分离条件的自相似集$T$ Lipschitz 等价,
则$U$与$T$也是 Lipschitz 等价. 并举例说明定理在自相似并集间的 Lipschitz 等价中的应用. |
| 英文摘要: |
| Let $U$ be a compact set satisfying a recurrence equation $U=(rU+\Theta)\cup U_1$,
which is a disjoint union.
The author proves that $U$ is Lipschitz equivalent to a self-similar set $T$ with the strong separated condition if $U_1$ is
Lipschitz equivalent to $T$. Some examples are provided to illuminate the application of the theory in the Lipschitz equivalence among the unions of self-similar sets. |
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