G. Gallavotti

Perturbation Theory for Classical Hamiltonian Systems

In Scaling and Self-Similarity, Ed. J. Fr\"ohlich, Birkhauser, 1983, p. 359--426

AbstractThe relation between the Kolmogorov-Arnold-Moser theory of the non resonant motions in nearly integrable Hamiltonian systems and the renormalization group methods is pointed out. It is followed by a very detailed proof of a version of the KAM theorem based on dimensional estimates (in which no attention is paid to obtaining best constants).

Keywords KAM, Renormalization Group, Quasi periodicity