东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2003, Vol. 24 ›› Issue (3): 237-240.DOI: -

• 论著 • 上一篇    下一篇

负幂次映射族广义M集的周期芽苞分布

邓学工;宋春林;李志勇;朱伟勇   

  1. 东北大学理学院;东北大学计算中心;东北大学计算中心;东北大学计算中心 辽宁沈阳110004
  • 收稿日期:2013-06-23 修回日期:2013-06-23 出版日期:2003-03-15 发布日期:2013-06-23
  • 通讯作者: Deng, X.-G.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目 ( 699740 0 8) ;;

Generalized M-set of complex mapping with negative power

Deng, Xue-Gong (1); Song, Chun-Lin (2); Li, Zhi-Yong (2); Zhu, Wei-Yong (2)   

  1. (1) Sch. of Sci., Northeastern Univ., Shenyang 110004, China; (2) Comp. Cent., Northeastern Univ., Shenyang 110004, China
  • Received:2013-06-23 Revised:2013-06-23 Online:2003-03-15 Published:2013-06-23
  • Contact: Deng, X.-G.
  • About author:-
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摘要： 利用吸引周期轨道存在与否为判断特征 ,给出了z-2 +c的广义M集的定义和其计算机构造方法· 同以往研究结果相比 ,用该定义构造的广义M集较好地反映了复映射族z-2 +c的动力学性质· 对不同构造方法所导致不同结果的原因进行了理论分析 ,同时给出了其周期芽苞的分类方法、数量计算公式和其占优周期芽苞分布的Fibonacci规律· 周期芽苞的分类方法为Julia集的研究提供了基础 ,周期芽苞数量计算公式和Fibonacci规律给出了z-2 +c的广义M集的轮廓· 其中Fi bonacci规律是M集与广义M集的核心性质

关键词: 周期轨道, 广义M集, Julia集, 逃逸时间算法, Lyapunov指数

Abstract: The generalized Mandelbrot-sets of complex mapping f(z,c)=z-2+c were defined and created by using a new method of periodic classification. The image of generalized Mandelbrot set of z-2+c was presented, and the period-buds were colored by different RGB. Compared with current methods (escape-time arithmetic and Lyapunov method), a more practicable exact arithmetic was given. The classification of periodic-buds was given. This classification gives a better understanding of the different topological structure of the buds with the same period. This classification presents a new method to distinguish the Julia sets by the position of the parameter. An formula of the exact number of period-buds was given and the Fibomacci sequence in the Mandelbrot set of complex mapping f(z,c)=z-2+c was found, Fibomacci sequence existed in any generalized Mandelbrot set of rational mapping.

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