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Fermi-Pasta-Ulam-Tsingou: When Paradox Turns into Discovery

Matteo Gallone
Friday, June 22, 2018 - 14:15

At the beginning of Enrico Fermi's scientific activity there is a study of the ergodic hypothesis in which he proved ergodicity for a generic dynamical system, generalising a theorem by Poincaré. Its proof was incomplete but, guided by physical intuition, he was anyway convinced of the result. In 1953-1954 he (together with J. Pasta, S. Ulam and M. Tsingou) started a series of numerical experiments to check that essentially any non-linearity would lead to a system satisfying the ergodic hypothesis.The outcome of the experiments was against the conjectured conclusion and a lot of effort has been spent in the last sixty years to understand the phenomenon, often paving the way to new fields of Mathematics and Physics (e.g. infinite dimensional integrable systems or prethermalisation).In this seminar I will introduce the problem, some basic notions of ergodic theory and I will try to show what the state of the art of the problem is trying to explain the most recent results.

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