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Abstract: . We present a new proof of a strengthened version of D.V. Anosov's multiphase averaging theorem, originally stated for systems of ODEs with slow variables evolving in R m 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 DiPerna-Lions ... (Update)
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BibTeX entry: (Update)
@misc{ dumas-multiphase,
author = "H. S. Dumas and F. Golse and P. Lochak",
title = "Multiphase Averaging for Generalized Flows on Manifolds",
url = "citeseer.ist.psu.edu/177970.html" }
Citations (may not include all citations):509 Sobolev Spaces (context) - Adams - 1975
44 Analyse fonctionnelle (context) - Brezis - 1983
21 transport theory and Sobolev spaces (context) - DiPerna, Lions et al. - 1989
10 Multiphase Averaging for Classical Systems (context) - Lochak, Meunier - 1988
1 Encyclopedia of Mathematical Sciences Vol (context) - Arnol, Ed - 1988
1 English translation: Functional Anal (context) - Bakhtin, multifrequency et al. - 1986
1 Averaging in multifrequency systems (context) - Dodson, Rynne et al. - 1989
1 On Anosov's averaging theorem (context) - Golse
1 the adiabatic theorem for the Hamiltonian system of differen.. (context) - Kasuga - 1961
1 Averaging in systems of ODEs with rapidly oscillating soluti.. (context) - Anosov - 1960
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