TY - JOUR
T1 - A geometric proof of the periodic averaging theorem on Riemannian manifolds
AU - Avendano-Camacho, Misael
AU - Davila-Rascon, Guillermo
N1 - Publisher Copyright:
© 2015, Universidad Complutense de Madrid.
PY - 2016/1
Y1 - 2016/1
N2 - 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.
AB - 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.
KW - Averaging method
KW - Perturbation theory
KW - Periodic flows
KW - Riemannian manifolds
KW - Horizontal lifts
KW - S-1-principal bundle
UR - http://www.scopus.com/inward/record.url?scp=84952986025&partnerID=8YFLogxK
U2 - 10.1007/s13163-015-0184-8
DO - 10.1007/s13163-015-0184-8
M3 - Artículo
SN - 1139-1138
VL - 29
SP - 169
EP - 189
JO - Revista Matematica Complutense
JF - Revista Matematica Complutense
IS - 1
ER -