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

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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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     author = {L. Galgani and A. Giorgilli},
     title = {Recent results on the {Fermi--Pasta--Ulam} problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {145--154},
     publisher = {mathdoc},
     volume = {300},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a12/}
}
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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/