A geometric proof of the periodic averaging theorem on Riemannian manifolds

Abstract

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 ${\mathbb{S}}^1$-action associated to this vector field is not necessarily trivial. We generalize the averaging procedure \cite{Arno-63,ArKN-88} 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.

The final publication is available at link.springer.com, Revista Matemática Complutense (2016)

References in corpus (2)

• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems
• Homological Equation for Tensor Field and Periodic Averaging