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Minimizing topological entropy for maps of the circle

  • Louis Block (a1), Ethan M. Coven (a2) and Zbigniew Nitecki (a3)

Abstract

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.

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Copyright

Corresponding author

Address for correspondence: Ethan M. Coven, Department of Mathematics, Wesleyan University, Middletown, Conn. 06457, USA.

References

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[1]Block, L.. Periodic orbits of continuous maps of the circle. Trans. Amer. Math. Soc. 260 (1980), 555562.
[2]Block, L.. Periods of periodic points of maps of the circle which have a fixed point. Proc. Amer. Math. Soc. 82 (1981), 481486.
[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. 1834. Northwestern, 1979. Lecture Notes in Math. no. 819. Springer: Berlin, 1980.
[4]Šarkovskii, A. N.. Co-existence of cycles of a continuous mapping of the line into itself. Ukrain. Mat. Ž. 16 (1964) 6171. (Russian, English summary.)
[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), 237248.

Minimizing topological entropy for maps of the circle

  • Louis Block (a1), Ethan M. Coven (a2) and Zbigniew Nitecki (a3)

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