FM 3-2018, arxiv:

Authors : Giovanni Gallavotti

Title:: Quasi periodic Hamiltonian Motions, Scale Invariance, harmonic Oscillators

Abstract: The work of Kolmogorov and Moser appeared just before the renormalization group approach to statistical mechanics was proposed by \cite{Wi971a}: it can be classified as a multiscale approach which also appeared in works on the convergence of Fourier's series, \cite{Ca966,Fe973}, or construction of Euclidean quantum fields, \cite{Ne966}, or the scaling analysis of the short scale behaviour of Navier-Stokes fluids, \cite{CKN982}, to name a few which originated a great variety of further problems. Here the proof of the KAM theorem will be presented as a classical renormalization problem with the harmonic oscillator as a ``trivial'' fixed point.

Keywords: KAM, Renormalization Group,

Giovanni Gallavotti
INFN-Roma1 and Universit\`a "La Sapienza” Roma, Italy