Orbit equivalence of linear systems on manifolds and semigroup actions on homogeneous spaces

Abstract

In this paper we introduce the notion of orbit equivalence for semi-group actions and the concept of generalized linear control system on smooth manifold. We prove that, under certain conditions, the semi-group system of a generalized linear control system on a smooth manifold is orbit equivalent to the semigroup system of a linear control system on a homogeneous space.