| 奇数分康托集与其平移并集的自相似性 |
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| 引用本文： | 李会平.奇数分康托集与其平移并集的自相似性[J].纺织高校基础科学学报,2010,23(2):195-201. |
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| 作者姓名： | 李会平 |
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| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062 |
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| 摘 要： | 考虑迭代函数系{fj(x)=(x+2j)/p}j(=p0-1)/2,其中p是奇数,且p≥3,则存在自相似集Ep,满足Ep=∪(p-1)/2j=0fj(Ep).讨论自相似集Ep与其平移Ep+β的并集的自相似性.证明方法从与奇数进制有关的引理入手,由特殊到一般给出一般表达式,最终得出β=2×pn为判断奇数分康托集与其平移的并集的自相似性提供了依据.
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| 关 键 词： | 自相似集 迭代函数系（IFS） 平移 |
Self-similarity of the union of odd-part Cantor set and its translation |
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| LI Hui-ping.Self-similarity of the union of odd-part Cantor set and its translation[J].Basic Sciences Journal of Textile Universities,2010,23(2):195-201. |
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| Authors: | LI Hui-ping |
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| Affiliation: | LI Hui-ping(College of Mathematics and Information Sciences,Shaanxi Normal University,Xi′an 710062,China) |
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| Abstract: | The iterated funtion system {fj（x）=（x＋2j）/p}j=0^（p-1）/2 is considered,p is an odd number,and p≥3,then there exists self-similar set Ep which satisfies
Ep=∪j=0^（p-1）/2fj（Ep）.Self-similarity of the union of the self-similar set Ep and its translation was discussed.Start with the lemma of the odd band,method of proof is from special to general,and the general expression was given.To provide a basis for judging the self-similarity of the union of odd-part Cantor set and its translation,β=2×p^n is gained finally. |
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| Keywords: | self-similar set iterated function system（IFS） translation |
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