复映射族f(z,c)=z^(-2)+c的Julia集  

Julia Set of Complex Mapping 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5期429-432,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(69974008);教育部博士学科点专项科研基金资助项目(2000014512)

摘　　要：给出了周期点分类构造Julia集的算法,克服用逃逸时间算法和反函数迭代法构造复映射族f(z,c)=z-2+cJulia集收敛不均匀的问题·研究了z-2+c不同参数对应Julia集的拓扑结构的演变规律,发现了不同性质的周期芽苞的点对应的Julia集的不同属性,给出了通过Julia集判断参数类型和通过参数位置预知Julia集拓扑结构的方法·提出了关于Julia集的连通性的一个猜想,并用大量计算机实验支持了这一猜想·?A new method,periodclassification algorithm,to get a better graphic of Julia sets of complex mapping z-2+c was given. Comparing with other algorithms such as escape time algorithm and inverse function algorithm, the periodclassification algorithm provides a better understanding of the dynamics of the complex mapping z-2+c. A large numbers of Julia sets of z-2+c were exhibited by use of a computer. Periodbuds were classified and the difference of the Julia sets in deferent periodbuds was studied. The period of the Julia set can be found and also the topological structure of the Julia set can be predicted by observing the position of the periodbud. A conjecture that all the Julia sets with 2 or higher periods are connected is presented. The conjecture is proved by lots of computer experiments.

关 键 词：复映射 JULIA集 周期分类法 周期芽苞 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]