| Engel连分数展式与Huasdorff维数 |
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| 引用本文： | 张振亮.Engel连分数展式与Huasdorff维数[J].应用数学,2011,24(3):641-644. |
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| 作者姓名： | 张振亮 |
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| 作者单位： | 华中科技大学数学与统计学院,湖北武汉,430074 |
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| 摘 要： | 本文研究了Engel连分数中部分商以某种速度增长的集合,以及Engel连分数展式收敛速度较快的点组成的集合,利用质量分布原理,证明了这些集合的Haus-dorff维数为1.
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| 关 键 词： | Engel连分数展式 Huasdorff维数 收敛速度 |
Engel Continued Fraction Expansion and Hausdorff Dimension |
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| ZHANG Zhenliang.Engel Continued Fraction Expansion and Hausdorff Dimension[J].Mathematica Applicata,2011,24(3):641-644. |
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| Authors: | ZHANG Zhenliang |
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| Institution: | ZHANG Zhenliang(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan430074,China) |
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| Abstract: | In this paper,we study a exceptional set determined by partial quotients in its Engel continued fraction expansion and the set consisting of the points whose speed of convergence is faster than thetypicalpoints.By using the principle of mass distribution,we prove that the Hausdorff di mension of these sets are both one. |
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| Keywords: | Engel continued fraction expansion Huasdorff dimension Speed of convengence |
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