| 一类非线性Cantor集维数的计算机估值 |
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| 引用本文： | 钟婷. 一类非线性Cantor集维数的计算机估值[J]. 数学杂志, 2006, 26(1): 71-74 |
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| 作者姓名： | 钟婷 |
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| 作者单位： | 吉首大学数学与计算机科学学院,湖南,张家界,427000 |
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| 摘 要： | 本文根据连分数性质及压缩变换的特征,给出了一类非线性Cantor集维数的估值算法,得到了其Hausdorff维数的较好上、下界.证明了只要计算机存储量足够,此上、下界可无限逼近维数的准确值.
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| 关 键 词： | 非线性Cantor集 连分数 Hausdorff维数 |
| 文章编号： | 0255-7797（2006）01-0071-04 |
| 收稿时间： | 2004-03-10 |
| 修稿时间： | 2004-03-102004-10-28 |
ESTIMATE OF THE NONLINEAR CANTOR SET DIMENSION |
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| ZHONG Ting. ESTIMATE OF THE NONLINEAR CANTOR SET DIMENSION[J]. Journal of Mathematics, 2006, 26(1): 71-74 |
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| Authors: | ZHONG Ting |
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| Affiliation: | College of Math and Computer Science, Jishou University, Zhang jiajie 427000, China |
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| Abstract: | According as the property of continued fractions an d the characterization of compress transform, the estimate arithmetic for the dime nsion of a Cantor set is presented in this paper. And the better upper and lower bounds of the Hausdorff dimension are obtained. So long as the memory of comput er is enough, the values of the upper and lower bounds will approach the accurat e values infinitely. |
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| Keywords: | nonlinear Cantor set continued fractions Hausdorff dimension |
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