{"paper":{"title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K Kaloshin, K Zhang, Patrick Bernard (DMA)","submitted_at":"2017-01-19T14:49:53Z","abstract_excerpt":"We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\\epsilon$H1($\\theta$, p, t), $\\theta$ $\\in$ T n , p $\\in$ B n , t $\\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly convex H0. We show that for a \"generic\" $\\epsilon$H1, there exists an orbit ($\\theta$, p)(t) satisfying p(t) -- p(0) {\\textgreater} l(H1) {\\textgreater} 0, where l(H1) is independent of $\\epsilon$. The diffusion orbit travels along a co-dimension one resonance , and the only obstruction to our construction is a finite set of additional resonances. For the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05445","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}