Statistical mechanics of weakly coupled oscillators presenting stochasticity thresholds

The present knowledge about dynamical properties of Hamiltonian systems of weakly coupled oscillators suggests the hypothesis of a transition to stochasticity through sharp energy thresholds. The latter hypothesis is shown here to lead in classical statistical mechanics to a possible removal of the so-called ultraviolet catastrophe, by following a line of thought which can quite naturally be attributed to Boltzmann himself. (author)