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On the transitive and $\omega$-limit points of the continuous mappings
of the circle

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*David Pokluda*

**Address.** Mathematical Institute, Silesian University, Opava, CZ
74601, CZECH REPUBLIC
**E-mail:** David.Pokluda@math.slu.cz

**Abstract.** 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.

**AMSclassification.** Primary 37E10, 26A18.

**Keywords. **Dynamical system, circle map, $\omega$-limit set, set
of transitive points.