Talk:Arnold diffusion

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Physics Low‑importance

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Essence of the idea

This article does not seem to describe the actual definition and essence of Arnold diffusion. Usually, Arnold diffusion is defined to be a specific diffusion of trajectories due to the ergodic theorem in a portion of phase space unbound by any constraints (ie tori due to constants of motion - action variables) in hamiltonian systems. It occurs in systems with more than N=2 degrees of freedom, since the N-dimensional invariant tori do not separate the 2N-1 dimensional phase space any more. Thus an arbitrarily small perturbation may cause a number of trajectories to wander pseudo-randomly through the whole portion of phase space left by the destroyed tori. 78.80.5.87 (talk) 18:00, 13 December 2012 (UTC)[reply]

Very well put. I copied the above almost verbatim into the article. 67.198.37.16 (talk) 19:15, 17 September 2020 (UTC)[reply]