A geometric proof of the periodic averaging theorem on Riemannian manifolds

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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 languageEnglish
Pages (from-to)169-189
Number of pages21
JournalRevista Matematica Complutense
Volume29
Issue number1
DOIs
StatePublished - Jan 2016

Keywords

  • Averaging method
  • Perturbation theory
  • Periodic flows
  • Riemannian manifolds
  • Horizontal lifts
  • S-1-principal bundle

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