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Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds

Abstract

For a right-invariant control system on a flag manifold \({\mathbb{F}_{\Theta}}\) of a real semisimple Lie group, we relate the \(\mathfrak{a}\)-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on \({\mathbb{F}_{\Theta}}\).

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Acknowledgements

The authors express their gratitude to Lino Grama for his help with the proof of Lemma A.2.

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Correspondence to Adriano Da Silva.

Additional information

AS was supported by FAPESP Grant 2016/11135-2 and a Guest Scientist Grant from the University of Passau, where part of this work was done.

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Da Silva, A., Kawan, C. Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds. Isr. J. Math. 232, 947–1000 (2019). https://doi.org/10.1007/s11856-019-1893-3

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