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.


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