Control Systems on Flag Manifolds and their chain Control sets
  In this paper we shown that the chain control sets of induced systems on flag manifolds coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. 
Victor Ayala, Adriano Da Silva and Luiz A.B. San Martin
math.DS