| Lyapunov exponents may be defined for noisy systems, as Giovanni proposed years ago. I will show that 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 regime, it offers an analytic glimpse on the regime in which many near-integrable systems, such as some planetary systems, find themselves in practice. |