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We focus on two approaches that have been proposed in recent years for theexplanation of the so-called FPU paradox, i.e. the persistence of energylocalization in the `low-q' Fourier modes of Fermi-Pasta-Ulam nonlinearlattices, preventing equipartition among all modes at low energies. In thefirst approach, a low-frequency fraction of the spectrum is initially excitedleading to the formation of `natural packets' exhibiting exponential stability,while in the second, emphasis is placed on the existence of `q-breathers', i.eperiodic continuations of the linear modes of the lattice, which areexponentially localized in Fourier space. Following ideas of the latter, weintroduce in this paper the concept of `q-tori' representing exponentiallylocalized solutions on low-dimensional tori and use their stability propertiesto reconcile these two approaches and provide a more complete explanation ofthe FPU paradox.

Energy localization on q-tori, long term stability and the interpretation of FPU recurrences