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In this paper we shown that the chain control sets of induced systems on flagmanifolds coincides with their analogous one defined via semigroup actions.Consequently, any chain control set of the system contains a control set withnonempty interior and, if the number of the control sets with nonempty interiorcoincides with the number of the chain control sets, then the closure of anycontrol set with nonempty interior is a chain control set.

Control Systems on Flag Manifolds and their chain Control sets