Journal of South China University of Technology(Natural Science Edition) ›› 2012, Vol. 40 ›› Issue (10): 142-145.doi: 1000-565X(2012)10-0142-04

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On Multifractal Analysis of Measures

Wu Min   

  1. Department of Mathematics,South China University of Technology,Guangzhou 510640,Guangdong,China
  • Received:2012-08-01 Online:2012-10-25 Published:2012-09-01
  • Contact: 吴敏(1956-) ，女，教授，博士生导师，主要从事分形几何研究． E-mail:wumin@ scut.edu.cn
  • About author:吴敏(1956-) ，女，教授，博士生导师，主要从事分形几何研究．
  • Supported by:

    国家自然科学基金资助项目( 10571063， 11071082)

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Abstract:

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 multifractal measures is of utmost importance.This paper briefly explains the basic ideas and methods of the multifractal analysis of measures and describes the author's major findings and achievements in this field.

Key words: multifractal, self-similar measure, Moran measure, doubling measure, pointwise dimension