关于上自相似集的三个定理  

Three theorems on super self-similar sets

作　　者：邓国泰[1] 刘春苔[2] 

机构地区：[1]华中师范大学数学与统计学学院,武汉430079 [2]武汉工业学院数理科学系,武汉430023

出　　处：《华中师范大学学报（自然科学版）》2008年第4期500-503,517,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(10771082).

摘　　要：修正了由Falconer所定义的上自相似集,然后通过构造,证明了上自相似集和自相似集并不相互唯一确定;存在非自相似的上自相似集,其Hausdorff维数与Box维数不相等.In the paper, the authors modified the definition of super self-similar set by Falconer, and then by constructions, they proved that the super self-similar set and selfsimilar set can＇t be determined by one another and that there exists a super self-similar sets which isn＇t self-similar such that its Hausdorff dimension isn＇t equal to its Box dimension.

关 键 词：自相似集 CANTOR集 上自相似集 

分 类 号：O174[理学—数学]