| Cantor集并的自相似性(英文) |
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| 引用本文： | 邓国泰,刘春苔.Cantor集并的自相似性(英文)[J].数学杂志,2011,31(5):847-852. |
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| 作者姓名： | 邓国泰 刘春苔 |
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| 作者单位： | 1. 华中师范大学数学与统计学学院,湖北武汉,430079
2. 武汉工业学院数理科学系,湖北武汉,430023 |
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| 基金项目： | Supported by National Natural Science Foundation of China(10771082) |
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| 摘 要： | 本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.
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| 关 键 词： | Cantor集 迭代函数系 自相似集 |
SELF-SIMILARITY OF UNIONS OF CANTOR SETS |
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| DENG Guo-tai,LIU Chun-tai.SELF-SIMILARITY OF UNIONS OF CANTOR SETS[J].Journal of Mathematics,2011,31(5):847-852. |
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| Authors: | DENG Guo-tai LIU Chun-tai |
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| Institution: | DENG Guo-tai 1,LIU Chun-tai 2 (1.School of Mathematics and Statistics,Huazhong Normal University,Wuhan 430079,China) (2.Department of Mathematics and Physics,Wuhan Polytechnic University,Wuhan 430023,China) |
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| Abstract: | In this article,the authors study the self-similarity of the union of Cantor sets.By the Cantor expressions they get a basic relationship between Cantor sets and iterated function systems:T ∪ (T + α) is a self-similar set iff there exists a natural number n ≥ 0,such that α =±(k2-k1)dn.Moreover,if T ∪ (T + α) is a self-similar set,it satisfies the open set condition. |
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| Keywords: | Cantor set iterated function system(IFS) self-similar set |
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