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Multiphase averaging for generalized flows on manifolds

Published online by Cambridge University Press:  19 September 2008

H. S. Dumas ,
F. Golse  and
P. Lochak
H. S. Dumas
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati OH 45221–0025, USA
F. Golse
Affiliation:
UFR de Mathématiques, Université Paris VII, Tour 45-55, 5e étage, 4 place Jussieu, 75251 Paris Cedex 05, France
P. Lochak
Affiliation:
DMI, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France
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Abstract

We present a new proof of a strengthened version of Anosov's multiphase averaging theorem, originally stated for systems of ODEs with slow variables evolving in Rm and fast variables evolving on a smooth immersed manifold. Our result allows the fast variables to belong to an arbitrary smooth compact Riemannian manifold, and the vector field to have only Sobolev regularity. This is accomplished using normal form techniques adapted to a slightly generalized version of the DiPema-Lions theory of generalized flows for ODEs.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 53 - 67
Copyright
Copyright © Cambridge University Press 1994

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References

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