ABSTRACT:

We consider the FPU problem in dimension higher than one. We stress some relevant differences with respect to the dimension one, and outline the possibility that in dimension larger than one, in the thermodynamic limit, the FPU problem disappears. Besides the classical FPU question, namely the rate of approach to equilibrium starting from initial conditions very far from equilibrium, we also describe here some recent studies, in one and higher dimensions, in which the statistics of the fluctuations around equilibrium is analyzed.