周期轨间蕴含关系的判定算法(Ⅰ)  

The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅰ)

作　　者：张景中[1] 杨路[1] 章雷 

机构地区：[1]中国科学院成都分院

出　　处：《应用数学和力学》1989年第11期977-985,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助课题

摘　　要：近年来,Sarkovskii定理及其有关研究引起很大兴趣.按Sarkovskii定理,若闭区向上连续自映射f有3-周期点,则对任意正整数n有n周期点.但f不可能有所有类型的n-周期轨.例如:则f仅有两种类型的3-周期轨中的一类.这表明Sarkovskii定理远远没有给出周期轨之间的关系的全部信息.本文(Ⅰ)中将给出周期轨的型的概念,并证明可从建立机械方法来判断一种周期轨是否蕴含另一类型的周期轨。本文(Ⅱ)中将给出这个判断方法的计算机程序,并列出一些计算结果.In recent years, there is a wide interest in Sarkovskii's theorem and the related study. According to Sarkovskii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must has an n-periodic orbit for any positive integer n But f can not has all n-periodic orbits for some n. For example, let Evidently,f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits. This explains that it isn't far enough to uncover the relation between periodic orbits by information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between two periodic orbits.

关 键 词：周期轨 连续自映射 蕴含关系 判定 

分 类 号：O189.1[理学—数学]