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Hyperbolic Chain Control Sets on Flag Manifolds

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Abstract

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.

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Notes

  1. In [21], it is falsely claimed that N +(Θ) centralizes \(\mathfrak {n}^{-}_{\Theta }\), which in general is not true.

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Acknowledgments

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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Authors and Affiliations

  1. Imecc - Unicamp, Departamento de Matemática Rua Sérgio Buarque de Holanda, 651 Cidade Universitária Zeferino Vaz, 13083-859, Campinas, SP, Brasil

    A. Da Silva

  2. Fakultät für Informatik und Mathematik, Universität of Passau, Innstraße 33, 94032, Passau, Germany

    C. Kawan

Authors
  1. A. Da Silva
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  2. C. Kawan
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Correspondence to A. Da Silva.

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Silva, A.D., Kawan, C. Hyperbolic Chain Control Sets on Flag Manifolds. J Dyn Control Syst 22, 725–745 (2016). https://doi.org/10.1007/s10883-015-9308-1

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  • DOI: https://doi.org/10.1007/s10883-015-9308-1

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