M-J混沌分形图谱中Misiurewicz点的分布规律

On the Distribution of Misiurewicz Points in M-J Chaos-Fractal Spectrum

利用计算机数学试验的方法研究了M-J混沌分形图谱中的准周期点——Misiurewicz点的性质及分布规律,得到了Misiurewicz点和M集周期芽孢的拓扑分布关系,给出Misiurewicz点和M集周期芽孢之间的递推公式,为进一步揭示M集的图像内部结构特征以及其内部的周期点、准周期点的性质提供了一个有益的探讨.

Using the method of computer mathematic experiments, the nature of Misiurewicz points as the preperiodic points in M-J chaos-fractal spectrum and their distribution are studied. The topological relationship between the distribution of Misiurewicz points and that of M-set periodic-buds is thus given, with a recursion formula between them derived. As a result, a useful discussion is made on revealing further the internal structure of M- set images and the properties of its periodic and perperiodic points.