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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

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For a class of multiphase averaging problems inwhich the unperturbed flow of the fast variables is a transitive Anosov flowor is ‘sufficiently rapidly mixing’, we obtain what we believe isan optimalpower-law estimate, in the small parameter, of the rate at which the averagemaximum difference between solutions of the exact and averaged problemsconverges to zero. This verifies and extends an earlier conjectural remark byV. I. Arnold.

Information

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