广义{m_(k)}-拟齐次Cantor集的Hausdorff维数介值性  

Intermediate value property of Hausdorff dimension of generalized{m_(k)}-quasi homogeneous Cantor sets

作　　者：宗文琦 莫利柳[1] ZONG Wenqi;MO Liliu(School of Mathematics and Information 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)》2023年第1期246-251,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：为了进一步探索Hausdorff维数的取值介于两最值之间的齐次Moran集的结构,引进了广义{m_(k)}-拟齐次Cantor集。运用质量分布原理讨论该类集合的Hausdorff维数,证明了对任意介于齐次Moran集Hausdorff维数的最大值与最小值之间的值,都存在一类广义{m_(k)}-拟齐次Cantor集,使得其Hausdorff维数与该值相等。In order to further explore the structure of homogeneous Moran sets whose Hausdorff dimension is between the maximum value and the minimum value,a special kind of homogeneous Moran sets,which is called the generalized{m_(k)}-quasi homogeneous Cantor sets,was defined.The Hausdorff dimension of the generalized{m_(k)}-quasi homogeneous Cantor sets was estimated by using the mass distribution principle.For any value between the maximum and the minimum value of the Hausdorff dimension of the homogeneous Moran sets,we proved that there is a class of generalized{m_(k)}-quasi homogeneous Cantor sets,whose Hausdorff dimension is equal to this value.

关 键 词：齐次MORAN集 HAUSDORFF维数 {m_(k)}-Moran集 广义{m_(k)}-拟齐次Cantor集 介值定理 

分 类 号：O174.12[理学—数学]