Journal of Dynamical and Control Systems

, Volume 22, Issue 4, pp 725–745 | Cite as

Hyperbolic Chain Control Sets on Flag Manifolds

  • A. Da Silva
  • C. Kawan


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.


Flag 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 [8] 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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Imecc - Unicamp, Departamento de Matemática Rua Sérgio Buarque de HolandaCampinasBrasil
  2. 2.Fakultät für Informatik und MathematikUniversität of PassauPassauGermany

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