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
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 244-249
- MSC: Primary 58F20; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0929418-0
- MathSciNet review: 929418