复映射f(z)=e^(iπ/2)+c广义M集及充满J集吸引周期轨道

GeneralMSets and Attracting Periodic Orbits of Filled-inJSets fromf(z)=e^(iπ/2)+c

目的探索非解析复映射f(z)=ei2πzw+c(其中c与w为复数)在参数平面上的广义M集的构造方法及动力平面上充满J集中的动力学特性.方法构造映射f(z)=ei2πzw+c的雅可比矩阵,求解在取定参数下的动力平面上使其雅可比矩阵行列式为零的点集.以该点集作为构造参数c平面上广义M集的初始迭代点集.发现各种指数w下c平面上M集的图形特征.研究M集上不同参数对其相应充满J集图形结构的影响.结果得出当w=n为正整数时的动力平面上吸引周期轨道中周期点按充满J集图形结构的层次分布的规律及其轨道特性.结论根据参数c在动力平面上的轨道特性确定映射f(z)=ei2πzw+c的广义M集.M集中包含大量的排列有序的周期区域.主M集上的参数与动力平面上的充满J集的图形结构有着明显的对应关系.如果构造充满J集的参数取自主M集,则吸引周期轨道的周期点将分布在充满J集的第一和第二层次上.

The Jacobin matrix of non-analytic complex mapping f（z）=e^iπ/2z^-w＋c , where c and w werecomplex number, was constructed for the purpose of solving the point set on the dynamical plane, satisfying the condition of zero value for the determinant of the matrix. The set was used as the initially-iterating-point set constructing general M set in the parameter C. The image characters of the M set in C plane, under the different value of power zv, were discussed. The effect of how the parameters chosen from different level bud-regions of different M sets affect the structure of filled-in J set was also discussed.When zv was posi- tive integer, the distribution character of periodic points of the attracting orbit in a filled-in J set was ob- served. That means if the parameter used to construct the filled-in J set was selected from the main M set region except the one-perlod region, the periodic points of the attracting orbit would be distributed in the first and second layers of the filled-in J set.