| THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅱ) |
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| 引用本文： | 张景中,杨路,章雷.THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅱ)[J].应用数学和力学(英文版),1990,11(2):139-147. |
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| 作者姓名： | 张景中 杨路 章雷 |
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| 作者单位： | Chengdu Branch,Academia Sihica,Chengdu,Chengdu Branch,Academia Sihica,Chengdu,Chengdu Branch,Academia Sihica,Chengdu |
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| 摘 要： | 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.
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| 收稿时间： | 1988-03-07 |
The criterion algorithm of relation of implication between periodic orbits (II) |
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| Zhang Jing-zhong,Yang Lu,Zhang Lei.The criterion algorithm of relation of implication between periodic orbits (II)[J].Applied Mathematics and Mechanics(English Edition),1990,11(2):139-147. |
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| Authors: | Zhang Jing-zhong Yang Lu Zhang Lei |
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| Institution: | Chengdu Branch, Academia Sihica, Chengdu |
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| Abstract: | In recent years, there is a wide interest in Sarkovskii's theorem and related study. According to Sarkovskii's theorem, if the continuous self-mapf of the closed interval has a 3-periodic orbit, thenf 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
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![$$f(x) = \left\{ {\begin{array}{*{20}c} {x + 1/2} \\ {2(1 - x)} \\ \end{array} } \right. \begin{array}{*{20}c} {x\varepsilon 0, 1/2]} \\ {x\varepsilon (1/2, 1]} \\ \end{array} $$](/content/L45055342911G2M5/10483_2005_Article_BF02014538_TeX2GIFE1.gif)