Quasi periodic Hamiltonian Motions, Scale Invariance, Harmonic Oscillators
Abstract
The work of Kolmogorov, Arnold and Moser appeared just before the renormalization group approach to statistical mechanics was proposed by Wilson: it can be classified as a multiscale approach which also appeared in works on the convergence of Fourier's series, or construction of Euclidean quantum fields, or the scaling analysis of the short scale behaviour of Navier-Stokes fluids to name a few which originated a great variety of further problems. In this review the proof of the KAM theorem will be presented as a classical renormalization problem with the harmonic oscillator as a `trivial' fixed point.
Keywords
Cite
@article{arxiv.1810.07786,
title = {Quasi periodic Hamiltonian Motions, Scale Invariance, Harmonic Oscillators},
author = {Giovanni Gallavotti},
journal= {arXiv preprint arXiv:1810.07786},
year = {2020}
}
Comments
FM05-18: v1-v.2-v.3 contained a mistake, now corrected (and simplified) here. In the new (version 5): symbol J_1 introduced in Eq.2.4, which is rewritten in a form suitable for the derivation of Eq.(5.4),(5.5). The latter although correct were not properly derived. Eq. 5.7 includes the bound on J_1 and the labels in the formulae of Sec.5 are updated