Circle maps having an infinite 𝜔-limit set which contains a periodic orbit have positive topological entropy

Chinen, Naotsugu

doi:10.1090/S0002-9939-03-06900-4

Circle maps having an infinite $\omega$-limit set which contains a periodic orbit have positive topological entropy
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by Naotsugu Chinen

Proc. Amer. Math. Soc. 131 (2003), 3547-3551

DOI: https://doi.org/10.1090/S0002-9939-03-06900-4

Published electronically: February 14, 2003

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Abstract:

Let $f$ be a continuous map from the circle to itself. The main result of this paper is that the topological entropy of $f$ is positive if and only if $f$ has an infinite $\omega$-limit set which contains a periodic orbit.

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