The application of centre manifolds to amplitude expansions. I. Ordinary differential equations |
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Authors: | Jack Carr Robert G Muncaster |
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Institution: | Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland;Department of Mathematics, University of Illinois, Urbana, Illinois 61801 USA |
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Abstract: | The theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics. |
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