一类一维齐次Moran集的维数结果  

Results of the dimensions of a class of one dimensional homogeneous Moran sets

作　　者：乔育 付晓慧 李彦哲[1] QIAO Yu;FU Xiao-hui;LI Yan-zhe(School of Mathematics and Informnation Science,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西大学学报(自然科学版)》2022年第2期551-556,共6页Journal of Guangxi University(Natural Science Edition)

基　　金：国家自然科学基金项目(11901121);广西自然科学基金项目(2020GXNSFBA297040)。

摘　　要：为了研究一维齐次Moran集的维数,利用由基本区间形成的连通分支构造了一类{m_(k)}-齐次Moran集,证明该类集合的packing维数和上盒维数在supk{m_(k)}<∞时为所有一维齐次Moran集对应维数的最小值。此外,对于该类集合的上盒维数,得到在一些条件下的取值范围,并找到其达到准确值的一个充分条件。In order to study the dimensions of one dimensional homogeneous Moran set,a class of homogeneous Moran set,{m_(k)}-homogeneous Moran set,is constructed by the connected components of the basic intervals,and the packing dimensions and the upper box dimensions of the sets are shown to obtain the minimum value of the one dimensional homogeneous Moran set under the condition sup k{m_(k)}<∞.Furthermore,the range of the upper box dimensions of the sets is obtained under some conditions,and a sufficient condition under which the upper box dimension gets the accurate value is found.

关 键 词：一维齐次Moran集 {m_(k)}齐次Moran集 上盒维数 PACKING维数 连通分支 

分 类 号：O189[理学—数学]