Understanding the FPU state in FPU–like models

Many papers investigated, in a variety of ways, the so-called "FPU state" Fermi-Pasta-Ulam model, namely state, intermediate between initial state and equipartition, that system soon reaches if initially one or few long-wavelength normal modes are excited. The FPU has been observed, particular, to obey characterizing scalings laws. aim this paper is twofold: First, reviewing commenting literature on suggesting possible way organize it. Second, contributing better understanding by studying similar Toda which provides, as known, closest integrable approximation FPU. As new tool, we analyze dimensionality invariant tori states corresponding observe it obeys main scaling law state.