THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅰ)

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-mapf of the closed interval has a3-periodic orbit.then f must has an n-periodic orbit for any positive integer n.But f can not hasall n-periodic orbits for some n.For example,letEvidently,f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits.This explains that it isn’t far enough to uncover the relation between periodic orbits byinformation which Sarkovskii’s theorem has offered.In this paper.we raise the concept oftype of periodic orbits.and give a feasible algorithm which decides the relation ofimplication between two periodic orbits.     

The criterion algorithm of relation of implication between periodic orbits (I)

In recent years, there is a wide interest in Sarkovskii’s theorem ami the related study. According to Sarkovskii’s theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic 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.     

THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅱ)

In recent years,there is a wide interest in Sarkovskii’s theorem and related study.According to Sarkovskii’s theorem,if the continuous self-map f of the closed interval has a3-periodic orbit,then f must has an n-periodic orbit for any positive integer n.But f can nothave all n-periodic orbits for some n.Example.LetEvidently f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits,whichexplains that it isn’t far enough to uncover the relation between periodic orbits by theinformation which Sarkovskii’s theorem has offered.In this paper,we raise the concept oftype of periodic orbits,and give a feasible algorithm which decldes the relation ofimplication between the two kinds of periodic orbits.     

线段自映射回归点的回归方式

有关线段自映射的回归点的研究是一维动力系统理论研究的一个重要课题.近年来这方面的工作已有不少成果发表,但多侧重于对回归点集的性质讨论.本文着重研究了回归点的回归方式.由此看出:在■arkovskii 序的意义下,线段自映射的回归点的回归方式与它的周期点的周期有着十分密切的联系.