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Summary:
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.
References:
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