A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations

Details A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations

2006-11-15

arxiv.org/abs/math-ph/0611035v2

Reviews in Mathematical Physics, Vol. 19, No. 6 (2007) 639-675

Physics

Mathematical Physics

33 pages, no figures

Scientific paper

10.1142/S0129055X07003085

We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.

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