| 一类弱自相似集的强正则性 |
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| 引用本文： | 祝颖润. 一类弱自相似集的强正则性[J]. 湖北大学学报(自然科学版), 2010, 32(2): 135-137 |
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| 作者姓名： | 祝颖润 |
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| 作者单位： | 华南理工大学,理学院,广东,广州,510640 |
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| 摘 要： | 自相似集和1中的Cookie-Cutter集具有强正则性,即它们的Hausdorff维数与Bouligand维数相等.考虑一类弱自相似集,在一定的条件下,利用隐含定理证明它们也具有强正则性.所获结果包含并推进了已有结果.
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| 关 键 词： | 弱自相似集 不变集 强正则性 |
Strong regularity of a kind of weak self-similar sets |
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| ZHU Yingrun. Strong regularity of a kind of weak self-similar sets[J]. Journal of Hubei University(Natural Science Edition), 2010, 32(2): 135-137 |
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| Authors: | ZHU Yingrun |
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| Affiliation: | ZHU Yingrun(School of Science,South China University of Technology,Guangzhou 510640,China) |
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| Abstract: | Self-similar sets and cookie-cutter sets in R^1 are strong regular,their Hausdorff and Bouligand dimensions are equal.In this paper,we considered a kind of weak self-similar sets.Using the implicit theorem,we derived that,under some certain conditions,weak self-similar sets were also strong regular,which extended the results of self-similar sets and cookie-cutter sets in R^1. |
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| Keywords: | weak self-similar set invariant set strong regularity |
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