| 可数无穷迭代函数系的分离性质 |
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| 引用本文： | 董新汉,童继稀.可数无穷迭代函数系的分离性质[J].湖南师范大学自然科学学报,2011,34(2):1-6. |
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| 作者姓名： | 董新汉 童继稀 |
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| 作者单位： | 湖南师范大学数学与计算机科学学院,中国,长沙,410081 |
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| 基金项目： | 国家自然科学基金资助项目，湖南省自然科学基金资助项目 |
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| 摘 要： | 主要讨论了可数无穷迭代函数系的分离性质.首先,考虑了非空紧子集X上的共形迭代函数系{Si}∞i=0,如果它满足有界畸变性质和弱分离条件,那么|Si(X)|→0.其次,研究了两类特殊的自相似无穷迭代函数系.其中一类中的吸引子是唯一的并且是紧的,并运用加权的关联矩阵来计算另一类的吸引子的豪斯道夫测度.最后,给出了满足分离性...
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| 关 键 词： | 无穷迭代函数系 豪斯道夫维数 有限型 弱分离条件 |
Separation Properties for Countably Infinite Iterated Function Systems |
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| DONG Xin-han,TONG Ji-xi.Separation Properties for Countably Infinite Iterated Function Systems[J].Journal of Natural Science of Hunan Normal University,2011,34(2):1-6. |
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| Authors: | DONG Xin-han TONG Ji-xi |
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| Institution: | DONG Xin-han(College of Mathematics and Computer Science,Hunan Normal University,Changsha,410081,China) |
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| Abstract: | The separation properties of countably infinite IFS is discussed. First, if the conformal IFS {Si} ∞i=0 on a nonempty compact subset X satisfies bounded distortion property and weak separation 'condition, then |Si(X)|→0. Second, two special classes infinite IFS of similitudes are investigated.The results include that the attractor of the infinite IFS {Si} ∞i=0 is unique and compact, and the Hausdorff dimension of other attractor is computed in terms of the spectral radius of certain weighted incidence matrix. Finally, some examples which satisfy the corresponding separation properties are given. |
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| Keywords: | infinite iterated function system(IFS) Hausdorff dimension finite type condition weak separation condition |
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