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Periodic orbits of continuous mappings of the circle without fixed points

Published online by Cambridge University Press:  19 September 2008

Chris Bernhardt
Chris Bernhardt
Affiliation:
Mathematics Department, Southern Illinois University, Carbondale, Illinois 62901, USA
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Abstract

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Let f be a continuous map of the circle to itself. Let P(f) denote the set of periods of the periodic points. In this paper the set P(f) is studied for functions without fixed points, so 1∉P(f). In particular, it is shown that if s, t are the two smallest integers in P(f) and s and t are relatively prime then αs+βt∈P(f) for any positive integers α and β.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 413 - 417
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Block, L.. Periodic orbits of continuous mappings of the circle. Trans. Amer. Math. Soc. 260 (1980), 553–561.CrossRefGoogle Scholar
[2]Block, L.. Periods of periodic points of the circle which have a fixed point. Proceedings of the A.M.S. (to appear).Google Scholar
[3]Block, L., Guckenheimer, J., Misiurewicz, M. & Young, L.. Periodic points and topological entropy of one dimensional maps. Global theory of dynamical systems. Lecture Notes in Maths. No. 819. Springer: Berlin, 1980.Google Scholar
[4]Newhouse, S., Palis, J. & Takens, F.. Stable families of dynamical systems. I: Diffeomorphisms. Preprint: IMPA, Brazil.Google Scholar
[5]Nitecki, Z.. Topological dynamics on the interval. Preprint: Tufts University.CrossRefGoogle Scholar