Zhang Jing-zhong, Yang Lu, Zhang Lei. The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅱ)[J]. Applied Mathematics and Mechanics, 1990, 11(2): 131-140.
 Citation: Zhang Jing-zhong, Yang Lu, Zhang Lei. The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅱ)[J]. Applied Mathematics and Mechanics, 1990, 11(2): 131-140.

# The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅱ)

• Publish Date: 1990-02-15
• 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.
•  [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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