  Upon initial excitation of a few normal modes the energy distribution among
all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits
exponential localization on large time scales. At the same time resonant
anomalies (peaks) are observed in its weakly excited tail for long times
preceding equipartition. We observe a similar resonant tail structure also for
exact time-periodic Lyapunov orbits, coined q-breathers due to their
exponential localization in modal space. We give a simple explanation for this
structure in terms of superharmonic resonances. The resonance analysis agrees
very well with numerical results and has predictive power. We extend a
previously developed perturbation method, based essentially on a
Poincare-Lindstedt scheme, in order to account for these resonances, and in
order to treat more general model cases, including truncated Toda potentials.
Our results give qualitative and semiquantitative account for the superharmonic
resonances of q-breathers and natural packets.
