Sommaire:

Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. The situation described here being `multi-resonance' -- by nature well beyond the Kolmogorov-Arnold-Moser and the Nekhoroshev regimes, it offers an analytic glimpse on the situation in which many near-integrable systems, such as some planetary systems, find themselves in practice.

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