周期轨间蕴含关系的判定算法(Ⅱ)*
The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅱ)
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摘要: 近年来,Sarkovskii定理及其有关研究引起很大兴趣.按Sarkovskii定理,若闭区间上连续自映射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,并证明可以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.Abstract: In recent years,there is a wide interest in Sarkovskii's theorem and related study.According to Sarkov.lkii'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 have all n-periodic orbits for some n.Example.Let Evidently,f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits,which explains that it isn't far enough to uncover the relation between periodic orbits by the 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 the two kinds of periodic orbits.
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[1] Sarkovskii.A.N.,Coexistence of cycles of a continuous map of the line into itself,Ukr.Math.Zh.,16(1964),61-71. [2] Stefan,P.,A theorem of Sarkovskii on the coexistence of periodic orbits of continuous endomorphisms of the real line,Comm.Math.Phys.,54(1977),237-248. [3] 张景中、杨路,关于Sarkovskii序的一些定理,数学进展,18,(1987),33-48. [4] 章雷,有限有序集上的自映射,学位论文(1987). [5] Coppel,W.A.,Sarkovskii-minimal orbits,Math.Proc.Camb.Phil.Soc.,93(1983).397-408. [6] Block,L.and D.Hart,Stratification of the space of unimodal interval maps,Ergod.Th.and Dynam.Sys.,3(1983),533-539. [7] Block,L,and D,Hart,Orbit tppes for maps of the interval,Ergod,Th,and Danam,Sps,,7(1987),161-164. [8] Bernhardt,C.,The ordering on permutations induced by continuous maps of the real line,Ergod,Th,and Danam,Sys,,7(1987),155-160. -
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