Abstract
© 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.
Original language | English |
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Pages (from-to) | 169-189 |
Number of pages | 21 |
Journal | Revista Matematica Complutense |
Volume | 29 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2016 |
Keywords
- Averaging method
- Perturbation theory
- Periodic flows
- Riemannian manifolds
- Horizontal lifts
- S-1-principal bundle