负幂次映射族广义M集的周期芽苞分布  

The General M-set of Complex Mapping with Negtive Power

作　　者：邓学工[1] 宋春林[2] 李志勇[2] 朱伟勇[2] 

机构地区：[1]东北大学理学院,辽宁沈阳110004 [2]东北大学计算中心,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2003年第3期237-240,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目 ( 699740 0 8) ;教育部高等学校博士学科点专项科研基金资助项目 ( 2 0 0 0 0 14 5 12 )

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FiThe general 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 general 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 exists in any general Mandelbrot set of rational mapping

关 键 词：负幂次映射族 周期芽苞 广义M集 JULIA集 逃逸时间算法 LYAPUNOV指数 吸引周期轨道 复动力系统 

分 类 号：O19[理学—数学]