| 有限型条件的刻画 |
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| 引用本文： | 王飞,邓起荣.有限型条件的刻画[J].山西师范大学学报,2009,23(3):20-23. |
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| 作者姓名： | 王飞 邓起荣 |
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| 作者单位： | 王飞(长治学院数学系,山西,长治,046011);邓起荣(福建师范大学数学与计算机科学学院,福建,福州,350007) |
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| 摘 要： | 若自相似迭代函数系{φj}^mj=1（满足φj（x）=ρjRjx＋bj,bj∈R^d，其中0〈ρj〈1，Rj为d×d正交矩阵）关于不变开集Ω满足有限型条件，K是迭代函数系{φj}^mj=1生成的自相似集．但是，Ω与K的交集可能为空集．本文用构造方法证明存在一个不变开集U，使得U∩K≠φ，且迭代函数系{φj}^mj=1关于不变开集U也满足有限型条件．
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| 关 键 词： | 迭代函数系 自相似集 不变开集 有限型条件 |
Characterization of the Finite Type Condition |
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| Institution: | WANG Fei, DENG Qi-rong ( 1. Department of Mathematics, Changzhi University, Changzhi 046011, Shanxi, China ; 2. School of Mathematical and Computer Sciences, Fujian Normal University, Fuzhou 350007, Fujian, China) |
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| Abstract: | If self-similar IFS {φj}^mj=1（ which satisfies： φj（x）=ρjRjx＋bj,bj∈R^d , where 0 〈 ρj 〈 1 , and Rj are orthonormal d×d matrices） satisfies finite type condition with respect to the invariant open set Ω. The invariant set K is generated by IFS {φj}^mj=1. Since the intersection of Ω and K may be empty. We prove that there exists an invariant open set U such that U∩K≠φ, and IFS {φj}^mj=1 also satisfies finite type condition with respect to the invariant open set U by a constructive method. |
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| Keywords: | iterated function systems self-similar sets invariant open set finite type condition |
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