The G^0-periodic points of a linear system

Victor Ayala, Adriano Da Silva

Published 2020-01-26Version 1

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