复映射族z^(-2)+c广义M集的标度性质  

Scaling Invariance of General Mandelbrot Set of f(z,c)=z^(-2)+c

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4期334-337,共4页Journal of Northeastern University(Natural Science)

基　　金：国家教育部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：在复映射 f(z,c) =z-2 +c的广义Mandelbrot集中 ,发现了主周期芽苞的标度规律·用符号动力学中的方法对其做了研究 ,给出了主周期芽苞字的规律 ,及字相应的提升方程 ,通过解字提升方程 ,给出了任意精确常数 μ的算法 ,通过大量的计算机计算得到了一个常数 μ =1 ·标度常数为 1的情况在复映射的标度常数研究中为首次发现·提出了常数In a general Mandelbrot set of complex mapping f(z,c)=z -2+c, a scaling constant μ was found. This constant was obtained by using the method of symbolic dynamics. The super-attracted points of the main periodic-buds were obtained by solving the word-lifting equations. The technique to solve the equations was introduced in detail. This scaling factor gives a better understanding of the Mandelbrot set of the complex maping z -2+c. The analogous phenomenon was also found at the boundary of other periodic buds. Using this method other scaling factor at the double-period bifurcation buds along the direction of real axis can be gotten. The scaling constant μ can be found at all tangential points of two buds. The scaling constant of double-period bifurcation could be a constant at any buds.

关 键 词：复映射 广义M集 符号动力学 分岔 标度 周期窗口 字提升法 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]