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.
出处
《华南理工大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
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)
关键词
重分形
自相似测度
MORAN测度
加倍测度
点态维数
muhifractal
self-similar measure
Moran measure
doubling measure
pointwise dimension
