线段上连续非混沌自映射某类点的性质

The Property of Periodic Point-Set of Non-Chaotic Self-Maps on Line-Segment[0,1]

线段I=[0,1]上的连续自映射混沌的充要条件是什么?这是一维动力系统中一个非常重要而又一直未能得到解决的问题,到目前为止,仍然有不少研究者致力于解决这一问题。对这一问题,本文继续在前文研究结果和思路的基础上,研究并得到了线段上连续非混沌自映射周期数集的PP(f)一个重要性质,从而为研究混沌充要条件提供了一个新途径。

What are the necessary-sufficient conditions for continuous self-maps chaos on the line segment I=[0,1]?It is an unsolved problem of importance in one dimensional dynamic system.By far,a lot of researchers are still working on it.In this paper,an important property of the periodic number-sets PP(f)of continuous non chaotic sef-maps on line segment I is obtained on the basis of previous research results and ideas.It will provide a new way to study the essence of chaos.