The chain recurrent set of flow of automorphisms on a decomposable Lie group

In this paper we show that the chain recurrent set of a flow of automorphisms on a connected Lie group coincides with the central subgroup of the flow, if the group is decomposable. Moreover, in the decomposable case, the flow satisfies the restriction property. Furthermore, the restriction of any flow of automorphisms to the connected component of the identity of its central subgroup is chain transitive.