Maps of the interval with every point chain recurrent

Block, Louis; Coven, Ethan M.

doi:10.1090/S0002-9939-1986-0857952-8

Maps of the interval with every point chain recurrent
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by Louis Block and Ethan M. Coven

Proc. Amer. Math. Soc. 98 (1986), 513-515

DOI: https://doi.org/10.1090/S0002-9939-1986-0857952-8

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Abstract:

We show that if $f$ is a continuous map of a compact interval to itself and every point is chain recurrent, then either ${f^2}$ is the identity map or ${f^2}$ is turbulent.

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