一类Moran测度的加细重分形分析  

Refined Multifractal Analysis for a Class of Moran Measures

作　　者：袁志会 占雨晴 YUAN Zhihui;ZHAN Yuqing(School of Science,East China University of Technology,330013,Nanchang,PRC)

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《江西科学》2023年第1期1-5,共5页Jiangxi Science

基　　金：国家自然科学基金项目(12061006);江西省自然科学基金项目(20212BAB201002);东华理工大学博士启动金项目(DHBK2019210)。

摘　　要：主要研究了在2种压缩方式和2种测度分配方式下的Moran集上的Moran测度的重分形分析。在假设2种方式的频率存在的前提下,得到了关于上、下局部维数所确定的水平集的Hausdorff维数和Packing维数,证明此类Moran测度满足重分形机制。The article focuses on the refined multifractal analysis for a class of Moran measures on Moran sets. The Moran sets and the measure are construct by two types of compression and distribution under the assumption that the existence of the frequencies of the two types. Both the Hausdorff and packing dimensions of the level sets indicating lower and upper local dimension will be considered. We prove that such Moran measures satisfy the multifractal mechanism.

关 键 词：MORAN测度 重分形分析 HAUSDORFF维数 PACKING维数 

分 类 号：O174.12[理学—数学]