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.
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)
