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

• 论文 • 上一篇    下一篇

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

刘向东1, 焉德军2, 朱伟勇2, 王光兴2   

  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
  • 收稿日期:1999-04-26 修回日期:2001-03-20 出版日期:2001-11-18 发布日期:2001-11-18
  • 通讯作者: XIE He-ping
  • 基金资助:
    the National Natural Science Foundation of China (69974008)

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)

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摘要： 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.

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.

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