Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (11): 1318-1324.

• Articles • Previous Articles     Next Articles

THE BOUNDS OF THE GENERAL M AND J SETS AND THE ESTIMATIONS FOR THE HAUSDORFF’S DIMENSION OF THE GENERAL J SET

LIU Xiang-dong1, YAN De-jun2, ZHU Wei-yong2, WANG Guang-xing2   

  1. 1. Department of Mathematics & Physics, Anshan Institute of Iron and Steel Technology, Anshan 114001, P.R.China;
    2. School of Information Science and Engineering, Northeastern University, Shenyang 110006, P.R.China
  • Received:1999-04-26 Revised:2001-03-20 Online:2001-11-18 Published:2001-11-18
  • Supported by:
    the National Natural Science Foundation of China (69974008)

Abstract: The bounds of the general M and J sets were analytically offered. Some of the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorithm, and followed from the conclusion, but also offered two estimations of some special Julia set’s Hausdorff’s dimension by approximate linearization method.

2010 MSC Number: 

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