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Da Silva, Adriano; Kawan, Christoph (2019): Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds. In: Israel Journal of Mathematics, Vol. 232, No. 2: pp. 947-1000
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Abstract

For a right-invariant control system on a flag manifold F-Theta of a real semisimple Lie group, we relate the alpha-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 F-Theta.