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

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MR Zbl
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 $M$.
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 
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
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[1] S. J. Agronsky A. M. Bruckner J. G. Ceder, T. L. Pearson: The structure of $\omega$-limit sets for continuous functions. Real Analysis Exchange 15 (1989-90), 483-510. | DOI | MR

[2] A. M. Bruckner J. Smítal: The structure of $\omega$-limit sets for continuous maps of an interval. to appear in Časopis pro Pěstování Mat. | MR

[3] M. J. Evans P. D. Humke C. M. Lee, R. J. O'Malley: Characterizations of turbulent one-dimensional mappings via $\omega$-limit sets. to appear.

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