一类广义Cantor集的Hausdorff维数与测度  

Hausdorff Dimension and Hausdorff Measure of a Class of General Cantor Sets

作　　者：王艳[1] 林琼[1] 

机构地区：[1]淮北煤炭师范学院数学科学学院,安徽淮北235000

出　　处：《淮北煤炭师范学院学报（自然科学版）》2010年第1期10-12,共3页Journal of Huaibei Coal Industry Teachers College(Natural Science edition)

摘　　要：讨论了线性迭代系统S1(x)=εx,S2(x)=ε2x+1-ε2,在满足开集条件时,产生的广义Cantor集F,并获得了F的Hausdorff维数s及Hausdorff测度的精确值.In this paper, a class of general Cantor sets F which are the attractors of the line iterated systems satisfying the open set condition is studied. We obtain that the Haussdorff dimensions and the exact Hausdorff measure values are such that s=logε√5-1/2,H^5（F）=1.

关 键 词：自相似映射 广义CANTOR集 HAUSDORFF维数 HAUSDORFF测度 

分 类 号：O189.1[理学—数学]