一个单峰函数族的模型

A MODEL FOR UNIMODAL MAPS

总的说来,人们对单峰函数族的动态性质已有较深刻的理解.如 MSS 序列的提出,周期窗口的发现,以及从不同角度对其动态性质的探讨都表明了这点.但是对参数所对应的函数拓扑熵大于零的混沌区域的结构还没有彻底研究清楚,本文讨论一个典型的单峰函数族,发现其混沌区域具有分层的结构,即可按层的次序把这个区域中的周期点、拟周期点和其他点的分布规律刻划出来.

A family of unimodal maps is given as the modelf_h(x)=(?)A periodic point of the model can be denoted by L(?)R^(β_1)…L^(α_m)R^(β_(?))CR,wherethe symbol L^(α_i)R^(β_i) is called s layer in this paper.Rules to describing tne distribution of the periodic points are constructed bylayers and the famous MSS sequence also obeys the rules.