title: Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition.
abstract: 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 a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.
authors.affiliation: Dipartimento di Matematica F. Enriques, Via Saldini 50, 20133 Milano, Italy. penati@mat.unimi.it
authors.forename: Tiziano
authors.initials: T
authors.lastname: Penati
authors.forename: Sergej
authors.initials: S
authors.lastname: Flach