| Engel连分数中一个例外集的Hausdorff维数 |
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| 引用本文： | 胡学海.Engel连分数中一个例外集的Hausdorff维数[J].数学杂志,2010,30(3). |
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| 作者姓名： | 胡学海 |
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| 作者单位： | 华中农业大学理学院,湖北,武汉,430074 |
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| 摘 要： | 本文研究了Engel连分数展式中部分商以某种速度增长的集合的Hausdorff维数.利用自然覆盖和质量分布原理,得到了集合B(α)={x∈(0,1):lim n→∞ log bn+1(x)/log bn(x)=α}的Hausdorff维数是1/α的结果.
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| 关 键 词： | Engel连分数展式 Hausdorff维数 |
HAUSDORFF DIMENSION OF AN EXCEPTIONAL SET IN ENCEL CONTINUED FRACTION EXPANSION |
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| HU Xue-Hai.HAUSDORFF DIMENSION OF AN EXCEPTIONAL SET IN ENCEL CONTINUED FRACTION EXPANSION[J].Journal of Mathematics,2010,30(3). |
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| Authors: | HU Xue-Hai |
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| Institution: | HU Xue-Hai (College of Science,Huazhong Agricultural University,Wuhan 430074,China) |
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| Abstract: | In this article, we study the Hausdorff dimension of an exceptional set determined by partial quotients in its Engel continued fraction expansion. By using natural coveting system and principle of mass distribution, we get the result that the Hansdorff dimension of the set B(α)={x∈(0,1):lim n→∞ log bn+1(x)/log bn(x)=α}ia 1/α. |
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| Keywords: | Engel continued fraction expansion Hansdorff dimension |
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