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)

  • Received Date: 1988-03-07
  • 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.
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