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arXiv · 0705.0804

The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria

S. Flach·A. Ponno
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Abstract

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.

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S. Flach, A. Ponno. 2007-05-07. The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria. https://doi.org/10.1016/j.physd.2007.11.017

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