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arXiv · 1512.05041

A geometric proof of the periodic averaging theorem on Riemannian manifolds

Misael Avendaño Camacho·Guillermo Dávila Rascón
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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.

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Misael Avendaño Camacho, Guillermo Dávila Rascón. 2015-12-16. A geometric proof of the periodic averaging theorem on Riemannian manifolds. https://doi.org/10.1007/s13163-015-0184-8

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