Massimiliano Guzzo, Giancarlo Benettin
A spectral formulation of the Nekhoroshev theorem and its relevance for 
numerical and experimental data analysis
(2220K, Postscript)

ABSTRACT.  In this paper we provide an analytical characterization of the Fourier 
spectrum of the solutions of quasi--integrable systems, which completes 
the Nekhoroshev theorem and looks particularly suitable to 
describe resonant motions. We also discuss the application of the result 
to the analysis of numerical and experimental data. The comparison of 
the rigorous theoretical estimates with numerical results shows a quite 
good agreement. It turns out that an observation of the spectrum for a 
relatively short time scale (of order $1/sqrt{\epsilon}$, where 
$\epsilon$ is a natural perturbative parameter) can provide 
informations on the behaviour of the system for the much 
longer Nekhoroshev times.