  Based on the Renormalization Group method, a reduction of non integrable
multi-dimensional hamiltonian systems has been performed. The evolution
equations for the slowly varying part of the angle-averaged phase space
density, and for the amplitudes of the angular modes have been derived. It has
been shown that these equations are precisely the Renormalization Group
equations. As an application of the approach developed, the modulational
diffusion in one-and-a-half degree of freedom dynamical system has been studied
in detail.
