The chain recurrent set for maps of the interval

Block, Louis; Franke, John E.

doi:10.1090/S0002-9939-1983-0687650-2

The chain recurrent set for maps of the interval
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by Louis Block and John E. Franke

Proc. Amer. Math. Soc. 87 (1983), 723-727

DOI: https://doi.org/10.1090/S0002-9939-1983-0687650-2

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Abstract:

Let $f$ be a continuous map of a compact interval into itself. We show that if the set of periodic points of $f$ is a closed set then every chain recurrent point is periodic.

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