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We study topological properties of semi-group actions on the circle byorientation-preserving homeomorhisms. We prove that a generic action eitherpossesses a forward-invariant interval-domain (i.e. a finite union of disjointcircle arcs), or is two-sided minimal (and, moreover, by a small perturbationone can create a map with arbitrary rotation number in the semigroup). For theminimal case, we also study conditions required for global synchronization.

Classification of generic semigroup actions of circle diffeomorphisms