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arXiv · 1803.05292

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

Adriano Da Silva·Christoph Kawan
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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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Adriano Da Silva, Christoph Kawan. 2018-03-14. Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds. https://arxiv.org/abs/1803.05292

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