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The aim of this paper is to give a condition to topological conjugacy ofinvariant flows in an Lie group $G$ which its Lie algebra $\mathfrak{g}$ isassociative algebra or semisimple. In fact, we show that if two dynamicalsystem on $G$ are hyperbolic, then they are topological conjugate.

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