Recent results on the Fermi-Pasta--Ulam problem
by L. Galgani and A. Giorgilli
We revisit the celebrated model of Fermi, Pasta and Ulam
with the aim of investigating the thresholds to equipartition in the
thermodynamic limit. 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.
presented at the "Workshop
on differential equations dedicated to the memory of Vladimir Lazutkin",
St.Petersburg, August 18-20, 2002.
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