Periodic points and topological entropy of maps of the circle

Bernhardt, Chris

doi:10.1090/S0002-9939-1983-0684649-7

Periodic points and topological entropy of maps of the circle
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Proc. Amer. Math. Soc. 87 (1983), 516-518 Request permission

Abstract:

Let $f$ be a continuous map from the circle to itself, let $P(f)$ denote the set of integers $n$ for which $f$ has a periodic point of period $n$. In this paper it is shown that the two smallest numbers in $P(f)$ are either coprime or one is twice the other.

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