04-350 A. Haro, R. de la Llave

A parameterization method for the computation of invariant tori and their whiskers in quasi periodic maps: numerical algorithms. (182K, latex) Nov 2, 04

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Abstract. We develop numerical algorithms for the computation of invariant manifolds in quasi-periodically forced systems. We show how to compute invariant tori and invariant manifolds associated to them. In particular, the stable and unstable manifolds of invariant tori, but also {\sl non-resonant} invariant manifolds associated to spaces invariant under the linearization. These non-resonant manifolds include the slow manifolds which dominate the asymptotic behavior. The algorithms are based on the parameterization method. Rigorous results about this method are proved in in a companion paper. In this paper, we concentrate on numerical issues of algorithm. Examples of implementations of the algorithms appear in another companion paper.

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