A geometric proof of the periodic averaging theorem on Riemannian manifolds

© 2015, Universidad Complutense de Madrid. We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the S1-action associated to this vector field is not necessarily trivial. We generalize the averaging procedure [2, 3] defining a global averaging method based on a free coordinate approach which allow us to formulate our results on any open domain with compact closure.