Geodesic
On the transitive and $\omega$-limit points of the continuous mappings of the circle
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 49-52.

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We extend the recent results from the class $\mathcal {C}(I,I)$ of continuous maps of the interval to the class $\mathcal {C}(\mathbb {S},\mathbb {S})$ of continuous maps of the circle. Among others, we give a characterization of $\omega $-limit sets and give a characterization of sets of transitive points for these maps.
Classification : 37B25, 37E10 
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     title = {On the transitive and $\omega$-limit points of the continuous mappings of the circle},
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Pokluda, David. On the transitive and $\omega$-limit points of the continuous mappings of the circle. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 49-52. http://geodesic.mathdoc.fr/item/ARM_2002__38_1_a4/