| 一类含参变量的Sierpinski垫片的Hausdorff测度 |
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| 引用本文： | 刘德华,袁红,伍庆军.一类含参变量的Sierpinski垫片的Hausdorff测度[J].大学数学,2008,24(4). |
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| 作者姓名： | 刘德华 袁红 伍庆军 |
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| 作者单位： | 临沂师范学院,数学系,山东,临沂,276000 |
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| 摘 要： | Sierpinski垫片是具有严格自相似性的经典分形集之一.本文给出了一类含参变量的Sierpinski垫片.通过它在x轴上的投影估计了这类Sierpinski垫片的Hausdorff测度的下界,然后精心构造了一个仿射变换,将参变量的范围由(0,π/3)的讨论转换到(π/3,π)的讨论,从而得到了这类Sierpinski垫片的Hausdorff测度的精确值.
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| 关 键 词： | Sierpinski垫片 迭代函数系 Hausdorff维数 Hausdorff测度 |
The Hausdorff Measure of a Class of Sierpinski Carpets with Parameter |
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| LIU De-hua,YUAN Hong,REN Qing-jun.The Hausdorff Measure of a Class of Sierpinski Carpets with Parameter[J].College Mathematics,2008,24(4). |
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| Authors: | LIU De-hua YUAN Hong REN Qing-jun |
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| Abstract: | Sierpinski carpet is one of the classic fractals with strict self-similar property.In this paper,we will give a class of Sierpinski carpets with parameter.The lower bound for the Hausdorff measure of this kind Sierpinski carpet with parameter is given by the project on x-axis.At the same time,through a skillful affine mapping that was constructed,we transfer the parameter which in the interval 0,π3 into the interval π3,π.Finally the exact value of the Hausdorff measure of these sets is obtained. |
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| Keywords: | Sierpinski carpet iterated function system Hausdorff dimension Hausdorff measure |
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