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  "body": "\n## Summary\n\nArnold diffusion is a slow drift of the action variables in a nearly [[integrable system|N0N7CMRCMH]] with three or more degrees of freedom.\nAlong such an orbit the actions change by an amount of order one, although the perturbation is arbitrarily small.\nIt shows that the stability given by [[KAM theory|3ZZSXKM16Z]] for most initial conditions does not hold for all of them.\nArnold gave the first example in 1964.\n\n## Explanations\n\n### L1 human\n\nIn a nearly integrable system most motions stay on invariant tori, which act like walls.\nWith two degrees of freedom these walls cut each energy level into separate rooms, so nothing can wander far.\nWith three or more degrees of freedom the walls are too thin to separate anything, like circles in three-dimensional space.\nThen an orbit can slip through the gaps between the tori and, very slowly, travel a long way.\nThis slow wandering is Arnold diffusion.\n",
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