Geodesic
The structure of $\omega$-limit sets for continuous maps of the interval
Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 42-47.

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We prove that every infinite nowhere dense compact subset of the interval $I$ is an $\omega$-limit set of homoclinic type for a continuous function from $I$ to $I$.
DOI : 10.21136/MB.1992.126240
Classification : 26A18, 37C70, 54H20, 58F12
Keywords: discrete dynamical system; continuous map; $\omega$-limit set; homoclinic set 
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Bruckner, Andrew M.; Smítal, Jaroslav. The structure of $\omega$-limit sets for continuous maps of the interval. Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 42-47. doi : 10.21136/MB.1992.126240. http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126240/

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