## On the number of control sets on compact homogeneous spaces.(English)Zbl 1079.22004

Let $$G$$ be a simply connected Lie group and let $$S$$ be a subsemigroup with nonempty interior that generates $$G$$. The authors give a method for determining the number of control sets on certain compact homogeneous manifolds over $$G$$. This is done by reducing the problem to the consideration of generalized flag manifolds over the semisimple factor arising in the Levi decomposition of $$G$$, where by previous results it can be carried out by a computation involving the Weyl group.

### MSC:

 22E15 General properties and structure of real Lie groups 22E46 Semisimple Lie groups and their representations 93B05 Controllability
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