A topological conjugacy of invariant flows on some class of Lie groups
  The aim of this paper is to give a condition to topological conjugacy of invariant flows in an Lie group $G$ which its Lie algebra $\mathfrak{g}$ is associative algebra or semisimple. In fact, we show that if two dynamical system on $G$ are hyperbolic, then they are topological conjugate. 
Alexandre J. Santana and Sim\~ao N. Stelmastchuk
math.DS