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

Abstract

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.

33 pages, no figures

References in corpus (6)

• A lecture on the classical KAM theorem
• Twistless KAM tori
• Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
• Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics
• KAM Theorem and Quantum Field Theory
• Renormalization group in Statistical Mechanics and Mechanics: gauge symmetries and vanishing beta functions

Cited by in corpus (3)

• Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems
• Asymptotic Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum
• Dual Lindstedt series and KAM theorem