The centralizer of Komuro-expansive flows and expansive actions

In this paper we study the centralizer of flows and -actions on compact Riemannian manifolds. We prove that the centralizer of every Komuro-expansive flow with non-resonant singularities is trivial, meaning it is the smallest possible, and deduce there exists an open and dense subset of geometric Lorenz attractors with trivial centralizer. We show that -actions obtained as suspension of -actions are expansive if and only if the same holds for the -actions. We also show that homogeneous expansive -actions have quasi-trivial centralizers, meaning that it consists of orbit invariant, continuous linear reparameterizations of the -action. In particular, homogeneous Anosov -actions have quasi-trivial centralizer.