构造变基本域的P1平面对称动力系统  

Construction of Dynamic System with P1 Plane Symmetry from the Mapping with Transformable Fundamental Region

作　　者：陈宁[1] 孙艳玲[1] 孙晶[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6期1099-1102,共4页Journal of Shenyang Jianzhu University：Natural Science

基　　金：辽宁省自然科学基金项目(20032005);沈阳市人才基金项目(2008140403010)

摘　　要：目的分析标准的平面结晶体群映射的特点,构造变周期窗口的可视化平面动力系统.方法将P1对称平面动力系统迭代公式中三角函数的线性角度变量x与y用非线性量x3+c1与y3+c2替换.运用蒙特卡罗搜索法选定参数向量,并通过李雅普诺夫指数确定动力系统的动力学特性.结果构造出了随参数变化而改变基本域尺度的P1平面对称动力系统.关于选定参数下的动力系统,动力平面上各周期窗口尺度是变化的,平面上的点向基本域投影为非线性的.结论提出了一个构造正方形格子平面排列的P1对称动力系统的方法,可以用于大量构造正方形平面排列的混沌吸引子和充满Julia集图案.To construct visualized planar dynamic systems with different sizes of cycle windows, the nonlinear item x^3 ＋ c1 or y^3 ＋ c2 is substituted for the angle variable of the linear item x or y in the trigonometry functions. Monte Carlo method is used to search the parameter vectors in the parameter space. The Lyapunov exponent is used to judge the characteristics of dynamical systems. For the P1 symmetric dynamical systems defined in this paper, the fundamental region in the dynamic plane will be included in the different intervals in x and y directions as the values Cl and c2 are changed. Furthermore, for given parameters, the measures for different cycle windows in the dynamic plane are different respectively. We present a method to construct symmetric dynamical systems which can be used to generate square plane tiling. A great of chaotic attractors and filled-in Julia sets in the fundamental regions can be continuously tiled without gaps in the plane.

关 键 词：平面结晶体群 非解析映射 混沌吸引子 充满JULIA集 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]