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We shall use a Renormalization Group (RG) scheme in order to prove theclassical KAM result in the case of a non-analytic perturbation (the latterwill be assumed to have continuous derivatives up to a sufficiently largeorder). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We shall finallyshow that the sequence of the approximate solutions will converge to adifferentiable solution of the original problem.Comment: 33 pages, no figure

A RENORMALIZATION PROOF OF THE KAM THEOREM FOR NON-ANALYTIC PERTURBATIONS