Coherent modes versus radiation in the Fermi-Pasta-Ulam chain

The FPU chain is a 1D chain of particles evolving via conservative, Hamiltonian dynamics. It has a huge physics literature starting with the work of F, P and U in 1947 to scrutinize some predictions of statistical mechanics, and many interesting scaling regimes connecting it to both hyperbolic conservation laws and dispersive dynamics depending on length and time scale. I will discuss rigorous results including the radiative decay of coherent initial data under linear dynamics and the existence of open sets for which coherent initial data survive for all times under nonlinear dynamics.