Jordan decomposition and the recurrent set of flows of automorphisms

Abstract

<p style='text-indent:20px;'>In this paper we show that any linear vector field <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{X} $\end{document}</tex-math></inline-formula> on a connected Lie group <inline-formula><tex-math id="M2">\begin{document}$ G $\end{document}</tex-math></inline-formula> admits a Jordan decomposition and the recurrent set of the associated flow of automorphisms is given as the intersection of the fixed points of the hyperbolic and nilpotent components of its Jordan decomposition.