Multifractal spectra of Moran measures without local dimension

被引：11
|
作者：
Yuan, Zhihui [1 ]
机构：
[1] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
来源：
NONLINEARITY | 2019年 / 32卷 / 12期
关键词：
multifractal; upper local dimension; lower local dimesnion;
D O I：
10.1088/1361-6544/ab45d7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of Moran measures and study their lower and upper local dimensions. We show that the related ?free energy? function (L-q-spectrum) does not exist. Nevertheless, we can obtain the full Hausdroff and packing dimension spectra for level sets defined by lower and upper local dimensions. They can be viewed as a generalized multifractal formalism.
引用
收藏
页码：5060 / 5086
页数：27
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