Zhang Jing-zhong, Yang Lu, Zhang Lei. The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅰ)[J]. Applied Mathematics and Mechanics, 1989, 10(11): 977-985.
 Citation: Zhang Jing-zhong, Yang Lu, Zhang Lei. The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅰ)[J]. Applied Mathematics and Mechanics, 1989, 10(11): 977-985.

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

• Publish Date: 1989-11-15
• 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.
•  [1] Sarkovskii,A.N.,Ukr.Mat.Z.,16(1964),6-71. [2] Stefan,P.,Comm.Math.Phys.,54(1977),237-248. [3] 张景中、杨路,数学进展,16, 1 (1987), 33-48. [4] 章雷,有限有序集上的自映射,数学学报.(待发表). [5] Block,L.and D.Hart,Ergod.Th.and Dynam.Sys.,3(1983),533-539.

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