A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations
Mathematical Physics
2009-11-11 v2 math.MP
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.
Cite
@article{arxiv.math-ph/0611035,
title = {A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations},
author = {Emiliano De Simone},
journal= {arXiv preprint arXiv:math-ph/0611035},
year = {2009}
}
Comments
33 pages, no figures