关于测度的重分形分析  

On Multifractal Analysis of Measures

作　　者：吴敏[1] 

机构地区：[1]华南理工大学数学系,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2012年第10期142-145,共4页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571063;11071082)

摘　　要：测度的重分形分析是分形几何的一个重要研究方向,它广泛应用于动力系统、湍流、降雨量模型、地震和金融时间序列模型.发展重分形测度的数学理论和方法至关重要.文中简要阐述测度的重分形分析的基本思想和方法,并介绍笔者及其课题组在该领域取得的主要研究成果.Multifractal analysis of measures is known as an important research direction of fractal geometry. It has been widely used in dynamical systems, turbulence analysis, rainfall modeling, earthquake analysis, and financial time series modeling. Developing the mathematical theory and methods of muhifractal measures is of utmost impor- tance. This paper briefly explains the basic ideas and methods of the muhifractal analysis of measures and describes the authorg major findings and achievements in this field.

关 键 词：重分形 自相似测度 MORAN测度 加倍测度 点态维数 

分 类 号：O29[理学—应用数学]