一类非线性Cantor集维数的计算机估值  

ESTIMATE OF THE NONLINEAR CANTOR SET DIMENSION

作　　者：钟婷[1] 

机构地区：[1]吉首大学数学与计算机科学学院,湖南张家界427000

出　　处：《数学杂志》2006年第1期71-74,共4页Journal of Mathematics

摘　　要：本文根据连分数性质及压缩变换的特征,给出了一类非线性Cantor集维数的估值算法,得到了其Hausdorff维数的较好上、下界.证明了只要计算机存储量足够,此上、下界可无限逼近维数的准确值.According as the property of continued fractions and the characterization of compress transform, the estimate arithmetic for the dimension of a Cantor set is presented in this paper. And the better upper and lower bounds of the Hausdorff dimension are obtained. So long as the memory of computer is enough, the values of the upper and lower bounds will approach the accurate values infinitely.

关 键 词：非线性Cantor集 连分数 HAUSDORFF维数 

分 类 号：O173.2[理学—数学]