Classical Electrodynamics as a nonlinear dynamical system

We report on preliminary investigations, of numerical and analytical character, on the dynamical properties of the classical Hamiltonian model for the interaction of electromagnetic radiation with a nonrelativistic charged point particle. We investigate the distribution of energy among the field normal modes when the energy is initially given to the particle, and we find that the high frequency modes have a tendency to be frozen, a fact that is in agreement with the qualitative trend expected from Nekhoroshev's theorem for systems of weakly coupled harmonic oscillators. Moreover we point out that, as a consequence of the dynamical interaction with the radiation field, the charged particle appears to have a highly fluctuating motion.