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 $${\mathbb{F}_{\Theta}}$$ .