构造具有Z_(n-1)对称的复动力系统  

Construction of Complex Dynamic System with Z_(n-1) Symmetry

作　　者：陈宁[1] 孙晶[1] 孙艳玲[1] 

机构地区：[1]沈阳建筑大学信息与控制工程学院,辽宁沈阳110168

出　　处：《沈阳建筑大学学报（自然科学版）》2008年第5期890-894,928,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：辽宁省自然科学基金项目(20032005)

摘　　要：目的构造具有Zn-1对称的复动力系统及其M集和充满Julia集.方法采用构造连续函数关于Zn对称群的共轭函数和的方法,构造出新的复解析映射,分析这个复映射的旋转对称的特点,确定映射的极值点与参数的对应关系,通过极值点的李雅普诺夫指数判断复动力系统的动力学特性.结果通过对选定参数下极值点的李雅普诺夫指数的测试,构造出了该复映射的具有n-1旋转对称形式的M集和广义充满Julia集.结论笔者构造的复映射可以用于构造Zn-1对称的复动力系统,其广义充满Julia集图形结构与经典的复映射的图形结构不同,为复动力系统的图形化研究提供了新的研究对象和新形式的分形图案.To get complex dynamical systems with Zn- 1 in Julia sets, we construct an analysis complex function cussing how to make a new continuous function by the symmetry , relating generalized M sets and filled - f（z） = z^n ＋ cz（c∈ C, n ∈ 3, 4, 5…） from dismethod of fp.G（x ） =∑σ∈G σ^-1（ P（ σ（ x ） ） ） , where P：R^2→R^2 is an arbitrary continuous function and G is a finite group, which was presented by Clifford A. Reiter in 2000. We investigate the characteristic of the rotational symmetry of the complex mapping family and the relation between the critical points and the parameter vectors. Lyapunov exponents from iterating critical pionts are used to judge the characters of the dynamic systems from the mappings. The generalized M sets and filled - in Julia sets of the mapping with n- 1 rotational symmetry are generated by the testing of Lyapunov exponents of the critical points of the dynamic systems with the chosen parameters. The complex mapping constructed in this paper can be used to make dynamic systems with Zn-1 symmetry. Because of the multi- critical - points, the graphic structure of filled - in Julia sets from this mapping is different from that of the classical complex mapping（z←z^n＋ c）.

关 键 词：复映射 对称群 分形 M集 充满JULIA集 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]