一类变形的McMullen集的维数及其应用  

Dimension of a Class of Modiffied Mc Mullen Sets and Its Application

作　　者：杨玉莲[1] 龙伦海[1] 

机构地区：[1]海南大学信息科学技术学院,海南海口570228

出　　处：《海南大学学报（自然科学版）》2010年第4期302-305,共4页Natural Science Journal of Hainan University

基　　金：海南省教育厅自然科学资助项目(Hjkj200406;Hj200308)

摘　　要：研究了平面上一类变形的Mc Mullen集R=∑∞k=1a00b-kxkyk,(xk,yk)R,其中整数a,b满足|a|≥|b|>1或者|b|≥|a|>1,有限整数点集R{(i,j),i=0,1,…,n-1,j=0,1,…,m-1},得到了这类自仿射集的Hausdorff维数和Box维数的计算公式.并且作为其应用给出了自仿射集R=∑∞k=1a bb a-kxkyk,(xk,yk)R相应的Hausdorff维数和Box维数,其中整数a,b满足|a-b|≥|a+b|>1或者|a+b|≥|a-b|>1有限整数点集R{(i+j,-i+j),i=0,1,…,|a-b|-1,j=0,1,…,|a+b|-1}.In the paper,a class of modified Mc Mullen sets R={∑∞k=1（a00b）-k（xkyk）/（xk,yk）R} was analyzed in which the integers satisfied ｜a｜≥｜b｜1 or ｜b｜≥｜a｜1 and the finite set {（i,j）/i=0,1,…,n-1,j=0,1,…,m-1}.and the Hausdorff dimension and Box dimension were obtained.As its application,the accordingly Hausdorff dimension and Box dimension for the following self-affine sets R={∑∞k=1（abba）-k（xkyk）/（xk,yk）R},were also obtained,in which a,b were integers satisfying ｜a-b｜≥｜a＋b｜1 or｜a＋b｜≥｜a-b｜1 and the finite set.R {（i＋j,-i＋j）/i=0,1,…,｜a-b｜-1,j=0,1,…,｜a＋b｜-1}.

关 键 词：表示系统 自仿射集 HAUSDORFF维数 BOX维数 

分 类 号：O174.12[理学—数学]