{"paper":{"title":"Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ke Zhang, Patrick Bernard, Vadim Kaloshin","submitted_at":"2011-12-13T02:08:43Z","abstract_excerpt":"In the present paper we prove a form of Arnold diffusion. The main result says that for a \"generic\" perturbation of a nearly integrable system of arbitrary degrees of freedom $n\\ge 2$ \\[ H_0(p)+\\eps H_1(\\th,p,t),\\quad \\th\\in \\T^n,\\ p\\in B^n,\\ t\\in \\T=\\R/\\T, \\] with strictly convex $H_0$ there exists an orbit $(\\th_{\\e},p_{e})(t)$ exhibiting Arnold diffusion in the sens that [\\sup_{t>0}\\|p(t)-p(0) \\| >l(H_1)>0] where $l(H_1)$ is a positive constant independant of $\\e$.\n  Our proof is a combination of geometric and variational methods. We first build 3-dimensional normally hyperbolic invariant c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2773","kind":"arxiv","version":2},"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"}