On the periodic points of a typical continuous function

Simon, K.

doi:10.1090/S0002-9939-1989-0929418-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the periodic points of a typical continuous function
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by K. Simon PDF

Proc. Amer. Math. Soc. 105 (1989), 244-249 Request permission

Abstract:

Let $n$ and $k$ be arbitrary natural numbers. We prove that for a typical continuous function $f$, every neighborhood of any periodic point of $f$ with period $n$ contains periodic points of $f$ with period $n \cdot k$.

References

S. J. Agronsky, A. M. Bruckner, and M. Laczkovich, Dynamics of typical continuous functions, J. London Math. Soc. (2) 40 (1989), no. 2, 227–243. MR 1044271, DOI 10.1112/jlms/s2-40.2.227
P. Humke and M. Laczkovich, Typical continuous functions are virtually nonmonotone, Proc. Amer. Math. Soc. 94 (1985), no. 2, 244–248. MR 784172, DOI 10.1090/S0002-9939-1985-0784172-7