一类广义Cantor集的Hausdorff维数  

Hausdorff dimension of generalized Cantor sets

作　　者：戴振祥[1] 

机构地区：[1]宁波教育学院,浙江宁波315000

出　　处：《浙江师大学报（自然科学版）》2001年第2期143-145,共3页Journal of Zhejiang Normal University(Natoral Sciences)

摘　　要：研究和推广了自相似分形中最经典的例子 Cantor三分集的构造及其 Hausdorff维数 ,利用满足开集条件的压缩自相似映射的性质 ,解决了一类广义 Cantor集的 Hausdorff维数计算问题 .主要结果是构造了一类广义的 Cantor-2 k+1 ( k∈ N)分集 ,并给出它们的维数 s=ln( k +1 ) / ln( 1 /ε) .It was introduced the construction of generalized Cantor set which was a classical case in self similar fractal and then its Hausdorff dimension was discussed,in order to work out the Hausdorff dimension of this type of generalized Cantor set,the quality of contraction self similar mapping that met the open set conditions was involved. It was also discussed construction of the generalized Contor 2k+1(k ∈N) fractal sets and their dimensions.

关 键 词：广义CANTOR集 HAUSDORFF维数 自相似映射 自相似分形 Cantor三分集 广义Cantor-2k+1分集 

分 类 号：O415.5[理学—理论物理]