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Minimizing topological entropy for maps of the circle

Published online by Cambridge University Press:  19 September 2008

Louis Block ,
Ethan M. Coven  and
Zbigniew Nitecki
Louis Block
Affiliation:
From the University of Florida, Gainesville, Fla.
Ethan M. Coven*
Affiliation:
Wesleyan University, Middletown, Conn.
Zbigniew Nitecki
Affiliation:
Tufts University, Medford, Mass.
*
†Address for correspondence: Ethan M. Coven, Department of Mathematics, Wesleyan University, Middletown, Conn. 06457, USA.
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Abstract

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For each n≥2, we find the minimum value of the topological entropies of all continuous self-maps of the circle having a fixed point and a point of least period n, and we exhibit a map with this minimal entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 145 - 149
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Block, L.. Periodic orbits of continuous maps of the circle. Trans. Amer. Math. Soc. 260 (1980), 555–562.CrossRefGoogle Scholar
[2]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
[3]Block, L., Guckenheimer, J., Misiurewicz, M., & Young, L.S.. Periodic points and topological entropy of one dimensional maps. In Global Theory of Dynamical Systems, Proceedings, pp. 18–34. Northwestern, 1979. Lecture Notes in Math. no. 819. Springer: Berlin, 1980.Google Scholar
[4]Šarkovskii, A. N.. Co-existence of cycles of a continuous mapping of the line into itself. Ukrain. Mat. Ž. 16 (1964) 61–71. (Russian, English summary.)Google Scholar
[5]Štefan, P.. A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line. Comm. Math. Phys. 54 (1977), 237–248.CrossRefGoogle Scholar