自相似集的质量分布原理与Hausdorff测度及其应用  

On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications

作　　者：许绍元[1] 周作领[2] 苏维宜[3] 

机构地区：[1]赣南师范学院数学与计算机科学学院,赣州341000 [2]中山大学岭南学院,广州510275 [3]南京大学数学系,南京210093

出　　处：《数学学报（中文版）》2010年第1期117-124,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10961003;10971236)

摘　　要：本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法,并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的.In this paper, the mass distribution principle for the self-similar sets satisfying the open set condition （OSC） is set up. As an application, we obtain a new method for computing the exact value of the Hausdorff measure for a class of self-similar sets satisfying OSC. In addition, we give two examples to show that the new method is effective and workable to compute the exact values of the Hausdorff measures of a class of self-similar sets satisfying OSC.

关 键 词：Hausdorff测度与Hausdorff测度维数 自相似集 开集条件 

分 类 号：O174.12[理学—数学]