Hyperbolic Chain Control Sets on Flag Manifolds
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In this paper, we characterize the hyperbolic chain control sets of a right-invariant control system on a flag manifold of a real semisimple Lie group. Moreover, we provide a formula for the invariance entropy of such sets, applying a recently established result that holds in a more general setting.
KeywordsFlag manifolds Right-invariant control systems Chain control sets Hyperbolicity Invariance entropy
Mathematics Subject Classification (2010)93C15 37D20 37C60 22E46
The results of this paper are essentially based on ideas of the doctoral thesis  of the first author. We thank his advisors Fritz Colonius and Luiz San Martin for many fruitful mathematical discussions. The second author also thanks Peter Quast for taking his time to answer many question about semisimple Lie groups and their flag manifolds. The first author was supported by FAPESP scholarship 2013/19756-8 and partially by CAPES grant no. 4229/10-0 and CNPq grant no. 142082/2013-9. The second author was supported by DFG fellowship KA 3893/1-1.
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