On the number of control sets on flag manifolds of the real simple Lie groups

In this paper we determine upper bounds for the number of control sets on flag manifolds of a real non-compact simple Lie group whose Lie algebra is a real form of a complex simple Lie algebra. The estimates for the number of control sets are based on the results of San Martin and Tonelli. They are determined by computing the orbits of a subgroup of the Weyl Group.