Central periodic points of linear systems

Abstract

In this paper we show that the compactness of the central subgroup G 0 associated with the drift of a linear system ΣG on a connected Lie group G is a necessary and sufficient condition for the boundedness of the G 0 -periodic points of ΣG. As a consequence, the control set containing the identity element of G is bounded if and only if G 0 is a compact subgroup.