Braga Barros, Carlos J.; Reis, Ronan A. On the number of control sets on compact homogeneous spaces. (English) Zbl 1079.22004 Port. Math. (N.S.) 60, No. 3, 359-371 (2003). 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. Reviewer: Jimmy D. Lawson (M.R. 2004i:93012) Cited in 1 Document MSC: 22E15 General properties and structure of real Lie groups 22E46 Semisimple Lie groups and their representations 93B05 Controllability PDF BibTeX XML Cite \textit{C. J. Braga Barros} and \textit{R. A. Reis}, Port. Math. (N.S.) 60, No. 3, 359--371 (2003; Zbl 1079.22004) Full Text: EuDML