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Periodic points of maps of degree one of a circle

Published online by Cambridge University Press:  19 September 2008

MichaŁ Misiurewicz
MichaŁ Misiurewicz
Affiliation:
Institute of Mathematics, Warsaw University, PKiN IX p. 00-901, Warsaw, Poland
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Abstract

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There is a theorem of Sarkovskii which characterizes the sets of periods of periodic points for continuous maps of an interval into itself. We give a similar characterization for continuous maps of degree one of a circle into itself.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 2 , June 1982 , pp. 221 - 227
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Ch. Bernhardt, . Periodic orbits of continuous mappings of the circle. Preprint. Carbondale, 1980.Google Scholar
[2]Ch. Bernhardt, . Periodic points and topological entropy of maps of the circle. Preprint. Carbondale, 1980.Google Scholar
[3]Block, L.. Periods of periodic points of maps of the circle which have a fixed point. Proc. Amer. Math. Soc. 82 (1981), 481–486.CrossRefGoogle Scholar
[4]Block, L., Guckenheimer, J., Misiurewicz, M. & Young, L.-S.. Periodic points and topological entropy of one-dimensional maps. Global Theory of Dynamical Systems. Lecture Notes in Mathematics No. 819, Springer, Berlin, 1980, pp. 18–34.CrossRefGoogle Scholar
[5]Hall, G. R.. A C∞ Denjoy counterexample. Ergod. Th. & Dynam. Sys. 1 (1981), 261–272.CrossRefGoogle Scholar
[6]Ito, R.. Rotation sets are closed. Math. Proc. Camb. Phil. Soc. 89 (1981), 107–111.CrossRefGoogle Scholar
[7]Jefremova, L. S.. Periodic points of a continuous map of a circle. Proc. IX int. conf. on Non-linear Oscillations, Kiev 1981, p. 121. (In Russian.)Google Scholar
[8]Newhouse, S., Palis, J. & Takens, F.. Stable families of dynamical systems, I: Diffeomorphisms. Publ. I.H.E.S. (To appear.)Google Scholar
[9]Nitecki, Z.. Differentiable Dynamics. MIT Press: Cambridge, Mass., 1971.Google Scholar
[10]Poincaré, H.. Oeuvres completes, t. 1. Gauthier-Villars: Paris 1952, pp. 137–158.Google Scholar
[11]Sarkovskii, A. N.. Coexistence of cycles of a continuous map of a line into itself. Ukr. Math. Zurn. 16 (1964), 61–71. (In Russian.)Google Scholar
[12]Štefan, P.. A theorem of Sarkovskii on the existence of continuous endomorphisms of the real line. Commun. Math. Phys. 54 (1977), 237–248.CrossRefGoogle Scholar