The Fermi–Pasta–Ulam problem: Periodic orbits, normal forms and resonance overlap criteria
✍ Scribed by S. Flach; A. Ponno
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 654 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0167-2789
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✦ Synopsis
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.