The Fermi-Pasta-Ulam problem at very low energies was studied in [88]. It is found that there is a new energy threshold above which the Chirikov criteria of overlapping resonances is satisfied. In this regime the equipartition in energy takes place for some number of low energy modes. This new threshold is much below the conventional border of Chirikov and Izrailev (1966, 1973) and the critical energy per particle goes to zero with the increase of the number of particles. The mechanism of chaos in this regime is related to the resonances between sound waves with almost a linear dispersion law due to which even weak nonlinearity can strongly affect the long time dynamics (similar effects were discussed in section 3.5.1). At the same time the results obtained in [88] show that a proximity to completely integrable models such as Toda lattice can strongly affect dynamics as it happens for the case of cubic nonlinearity. Similar results were independently obtained by De Luca, Lichtenberg and Lieberman at Berkeley.