Geodesic
Recent results on the Fermi–Pasta–Ulam problem
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 145-154 Cet article a éte moissonné depuis la source Math-Net.Ru

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The celebrated model of Fermi, Pasta, and Ulam with the aim of investigating the thresholds to equipartition in the thermodynamic limit is revisited. Starting with a particular class of initial conditions, i.e., with all the energy on the first mode, we observe that in a short time the system splits in two separate subsystems. We conjecture the existence of a function $\epsilon_c(\omega)$, independent on the number $N$ of particles in the chain, such that if the initial energy $E$ satisfies $E/N<\epsilon_c(\omega)$ then only the packet of modes with frequency not exceeding $\omega$ shares most of the energy. 
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L. Galgani; A. Giorgilli. Recent results on the Fermi–Pasta–Ulam problem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 145-154. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a12/

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