上半平面极限映射的广义M集  

Generalized M Sets from Mapping with Upper Halfplane Limit

作　　者：陈宁[1] 金媛媛[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）》2007年第1期151-156,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：辽宁省自然科学基金(20032005);沈阳市科技局基金(200143-01)

摘　　要：目的为了对上半平面极限映射的参数空间进行有效划分,构造出了相应的广义M集.方法运用最优化理论中的步长加速算法,求解在选定参数下使得映射Jacobin矩阵的行列式值为零的点作为动力平面上的初始迭代点集,考察这个初始迭代点集中各点轨道的李雅普诺夫指数值,构造上半平面极限映射的广义M集,并进一步对其按相应的动力学特性的最大周期数进行周期区域划分.结果通过在这种广义M集上选取参数,可以大量生成内部结构各异的具有上半平面极限对称特性的广义充满Julia集及相应的方极限图案.结论运用步长加速算法构造的上半平面极限映射的广义M集实现了对参数空间的有效划分.To effectively divide the parameter space of the mapping of upper halfplane limit, we construct relevant generalized M sets. The accelerated direct search algorithm is used to search the set of initial iterating points, which make the absolute of Jacobin matrix values of the mapping with upper halfplane limit equal to zero, and M sets are constructed according to the dynamic characters of these points. From the M sets we can clearly see that the regions of chaos, period and the mix of chaos and period, We divide the periodic region in M sets basing on the maximum of periodic number of the orbits of the initial iterating points in the dynamic plane. The M sets have some similar characteristic with the classical M set. Various kinds of generalized filled-in Julia sets of upper halfplane limit and square limit, whose interior structure are greatly different, can be generated by choosing the parameters from different period area of the M sets.

关 键 词：混沌 上半平面极限映射 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]