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The averaging method for perturbations of mixing flows

Published online by Cambridge University Press:  01 December 1997

H. SCOTT DUMAS  and
FRANÇOIS GOLSE
H. SCOTT DUMAS
Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, OH 45221–0025, USA
FRANÇOIS GOLSE
Affiliation:
School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
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Abstract

For a class of multiphase averaging problems in which the unperturbed flow of the fast variables is a transitive Anosov flow or is ‘sufficiently rapidly mixing’, we obtain what we believe is an optimal power-law estimate, in the small parameter, of the rate at which the average maximum difference between solutions of the exact and averaged problems converges to zero. This verifies and extends an earlier conjectural remark by V. I. Arnold.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 6 , December 1997 , pp. 1339 - 1358
Copyright
1997 Cambridge University Press

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