Geodesic
On the fixed points in an $\omega$-limit set
Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 349-364.

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Let $M$ and $K$ be closed subsets of [0,1] with $K$ a subset of the limit points of $M$. Necessary and sufficient conditions are found for the existence of a continuous function $f:[0,1]\rightarrow [0,1]$ such that $M$ is an $\omega$-limit set for $f$ and $K$ is the set of fixed points of $f$ in $M$.
DOI : 10.21136/MB.1992.126065
Classification : 26A18, 54C30, 54H25
Keywords: $\omega$-limit set; fixed points 
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Ceder, J. G. On the fixed points in an $\omega$-limit set. Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 349-364. doi : 10.21136/MB.1992.126065. http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126065/

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