A topological conjugacy of invariant flows on some class of Lie groups

Abstract

The aim of this paper is to classify invariant flows on Lie group $G$ whose Lie algebra $\mathfrak{g}$ is associative or semisimple. Specifically, we present this classification from the hyperbolicity of the lift flows on $G \times \mathfrak{g}$. Then we apply this construction to some special cases as ${\rm Gl}(2,{\Bbb R})$ and affine Lie group.