A 𝐶¹ function for which the 𝜔-limit points are not contained in the closure of the periodic points

D’Aniello, Emma; Steele, T.

doi:10.1090/S0002-9947-03-03258-6

A $C^1$ function for which the $\omega$-limit points are not contained in the closure of the periodic points
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by Emma D’Aniello and T. H. Steele PDF

Trans. Amer. Math. Soc. 355 (2003), 2545-2556 Request permission

Abstract:

We develop a $C^1$ function $f: [- \frac {1}{6}, 1] \rightarrow [- \frac {1}{6}, 1]$ for which $\Lambda (f) \not = \overline {P(f)}$. This answers a query from Block and Coppel (1992).

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