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

TL;DR

This paper characterizes the chain recurrent set of automorphism flows on decomposable Lie groups, showing it coincides with the central subgroup and establishing properties like restriction and chain transitivity.

Contribution

It provides a precise description of the chain recurrent set for flows on decomposable Lie groups and proves the flow satisfies the restriction property in this setting.

Findings

Chain recurrent set equals the central subgroup in decomposable Lie groups.

Flow satisfies the restriction property in the decomposable case.

Flow restricted to the identity component of the central subgroup is chain transitive.

Abstract

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.