Koch曲线和Sierpinski垫片的Hausdorff测度的估计  

ESTIMATION OF HAUSDORFF MEASURES OF KOCH CURVE AND SIERPINSKI GASET

作　　者：瞿成勤[1] 苏维宜[1] 王衍波 

机构地区：[1]南京大学数学系,江苏南京210093 [2]通讯工程学院数学教研室,江苏南京210016

出　　处：《南京大学学报（自然科学版）》2000年第4期397-402,共6页Journal of Nanjing University（Natural Science）

基　　金：国家攀登计划!非线性科学 !(92 10 10 90 )

摘　　要：Koch曲线和Sierpinski垫片是两个经典的满足开集条件的自相似分形集。由自相似分形集的维数公式知 ,它们的Hausdorff维数分别是log34和log2 3。然而它们的Hausdorff测度的计算却是一个非常困难的问题。首先构造Koch曲线和Sierpinski垫片的特殊覆盖 ,然后对这种覆盖进行处理 ,根据自相似分形集的Hausdorff测度的齐次性质 ,分别给出了Koch曲线和Sier pinski垫片Hausdorff测度的上限 ,它改进了文献 [2～ 4 ]的相应结果 .Both Koch curve and Sierpinski gaset are two of the classical self similar sets satisfying the open set conditions. Their Hausdorff dimensions are log 3 4 and log 2 3, respectively. However, the calculations of their Hausdorff measures are very difficult open problem. In this paper, firstly, we construct the special coverings of Koch curve and Sierpinski gaset, and then improve these coverings. By the homogeneous property of the Hausdorff measure of the self similar set, the certain upper bounds of the Hausdorff measures of Koch curve and Sierpinski gaset are obtained, which improve the results of refs.[2～4].

关 键 词：KOCH曲线 SIERPINSKI垫片 HAUSDORFF测度 

分 类 号：O174.12[理学—数学]