FM 99-7; archived in mp_arc 99-???, chao-dyn/9907???
Last update: July 12, 1999

Authors: G. Gentile

Title: Diagrammatic techniques in perturbations theory, and
applications

Abstract:

We want to discuss an approach to the study of perturbed systems in
Classical Mechanics, based on methods characteristic of Quantum Field
Theory (QFT).  The starting point is to consider the perturbative
expansion of the solution of the equations of motion: this leads to
formal power series in the perturbative parameter, which were already
considered and studied in the old papers by Newcomb, Lindstedt and
Poincar\'e at the end of the last century.  The novelty consists in
applying to the study of such expansions techniques and tools which have
been developed only recently (with respect to the quoted authors) in
QFT, so in a very different field of Mathematical Physics.  Applications
and original results are briefly discussed.

Keywords: KAM tori, Perturbation theory, Quantum Field Theory

G.G.: Dipartimento di Matematica, Universita' Roma Tre, Largo S. Leonardo
      Murialdo 1, 00146 Roma (Italia)
      gentile@matrm3.mat.uniroma3.it