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Whether typical systems actually drift that fast, and with which exponent, is open.","posed_since":"","precise":"For analytic $H = h(I) + \\epsilon f$ with $h$ convex in $n$ degrees of freedom, Nekhoroshev gives $\\left|I(t) - I(0)\\right| \\le C \\epsilon^b$ for $\\left|t\\right| \\le \\exp(c \\epsilon^{-a})$ with optimal $a = 1/(2n)$. Prove that for generic $f$ there are orbits drifting by order one in time $\\exp(C \\epsilon^{-1/(2n)})$, matching the upper bound. Answer: a proof of the matching lower bound or a counter-argument.","problem_ref":"2c9684024cce20a0c9050aaf7f0a9e029a707487b6951500e5a44cd0504281b4","references":"","settled_by":"A construction of diffusing orbits with time $\\exp(C \\epsilon^{-1/(2n)})$ for an open set of perturbations.","status_note":"Specific analytic perturbations with diffusion time exponentially long in a power of 1/eps near the Nekhoroshev exponent were built by Ke Zhang (Inventiones Mathematicae, 2011); matching bounds for generic f are open.","title":"Optimal diffusion time compared with the Nekhoroshev stability 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