Linearization of a quasi-periodically forced flow on ?m under Brjuno-Russmann non-resonant condition

In this paper, we prove that a class of quasi-periodically forced flow with external parameters on a m-torus is linearizable, i.e. conjugable to the quasi-periodic rotation, under some appropriate conditions. More concretely, utilizing Poschel-Russmann KAM method we can find a quasi-periodic transformation such that this flow becomes a quasi-periodic linear flow in a Cantor subset of parameters when forcing frequency to satisfy the Brjuno-Russmann's non-resonant condition and a weaker non-degeneracy condition, respectively. While in the case where the unperturbed rotation vector does not satisfy the weaker non-degeneracy condition, Herman's method is applied to overcome the degeneracy so that we show that some perturbed systems can conjugate to the original system with prescribed rotation vector Finally, as an application, our results are used to investigate the spectrum and eigenfunctions of a quasi-periodic Schrodinger operators.