Control systems on flag manifolds and their chain control sets
Victor Ayala Adriano Da Silva Luiz A. B. San Martin

A right-invariant control system $Σ$ on a connected Lie group $G$ induce affine control systems $Σ_{Θ}$ on every flag manifold $\mathbb{F}_{Θ}=G/P_{Θ}$. In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. Some relevant examples are included.

keywords: Semigroups control systems flag manifolds chain control sets
Topological conjugacy of linear systems on Lie groups
Adriano Da Silva Alexandre J. Santana Simão N. Stelmastchuk

In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.

keywords: Topological conjugacy linear vector fields flows Lie groups Lyapunov exponents

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