{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"848b08e708c8019c2f781ed438d0766063fd602e4b72fd1cc1621cd72b009a32","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"22a90f7a6afeb127b8b2664775e65578093f99bde928cb0f699aecf9ce38ec94","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.kam-stability.generic-arnold-diffusion","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Arnold conjectured that in typical nearly regular systems with three or more degrees of freedom, some orbits drift by a finite amount no matter how small the perturbation. This is proven only in a weaker sense of typical, or for low numbers of degrees of freedom.","posed_since":"1964","precise":"$H = h(I) + \\varepsilon f(\\theta, I)$, (theta, I) in T^n x R^n, h strictly convex, $n \\ge 3$. Prove that for generic f (residual in $C^r$, r large; separately, for an open set of analytic f) and all small $\\varepsilon > 0$ there are orbits with $\\mid I(T) - I(0) \\mid \\ge c$ with c independent of $\\varepsilon$. Answer: a proof for every $n \\ge 3$.","problem_ref":null,"references":"","settled_by":"A proof valid for arbitrary n with residual (or analytic open) genericity.","status_note":"Proven for two and a half degrees of freedom for cusp-residual $C^r$ perturbations (Kaloshin and Zhang, Annals of Mathematics Studies 2020; Cheng); arbitrary n in a weaker cusp-residual sense (Bernard, Kaloshin and Zhang, Acta Mathematica 2016); genuinely residual or analytic perturbations remain open.","title":"Arnold diffusion for generic nearly integrable systems","topic_ref":"cd1c7cff821fba931816a6faeec94ad21e6f069bd36505c710e41ce43b61e40a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"cf126bf977bf78a7d7f9b4dcf3fb05b0611f3281a1ed56cb6f60af31d3e2df66","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0a54754b5ae46ae71c57d148bf85509b8f598cff1c17ab350410d656bc0cb0b7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"CSTva2je683j-c-mR9uvUMjfOoEJlLk_wQLems2ZFh1wfe1D8mloi1EwSYFc6KS9UsjPkKIENt9PxwnUNX8HBQ"},"schema":"pubphys.envelope/1"},"record_hash":"cf126bf977bf78a7d7f9b4dcf3fb05b0611f3281a1ed56cb6f60af31d3e2df66","leaf_index":1635}