  Fermi, Pasta and Ulam observed, that the excitation of a low frequency normal
mode in a nonlinear acoustic chain leads to localization in normal mode space
on large time scales. Fast equipartition (and thus complete delocalization) in
the Fermi-Pasta-Ulam chain is restored if relevant intensive control parameters
exceed certain threshold values. We compare recent results on periodic orbits
(in the localization regime) and resonant normal forms (in a weak
delocalization regime), and relate them to various resonance overlap criteria.
We show that the approaches quantitatively agree in their estimate of the
localization-delocalization threshold. A key ingredient for this transition are
resonances of overtones.
