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

David Pokluda

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.