| The aim of the talk is to revisit, in the light of some recent numerical results, some old ideas concerning the FPU problem, namely (i) The presence, in the so called "alpha-model" (dominant cubic nonlinearity), of at least two well separated time scales: a short one, where only a few normal modes share energy, and a larger one, where energy equipartition among all normal modes occurs and the behavior of the model, in view of Statistical Mechanics, is regular. (ii) The fact that in the short time scale the dynamics of FPU, in spite of the partial energy sharing, is essentially integrable and practically coincides with the dynamics of the Toda model, while in the large time scale nonintegrability becomes manifest. The role of the constants of motion of the Toda model in the FPU dynamics will be also discussed. |