{"paper":{"title":"A strong form of Arnold diffusion for two and a half degrees of freedom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ke Zhang, Vadim Kaloshin","submitted_at":"2012-12-05T20:28:09Z","abstract_excerpt":"In the present paper we prove a strong form of Arnold diffusion. Let $\\mathbb{T}^2$ be the two torus and $B^2$ be the unit ball around the origin in $\\mathbb{R}^2$. Fix $\\rho>0$. Our main result says that for a \"generic\" time-periodic perturbation of an integrable system of two degrees of freedom \\[ H_0(p)+\\epsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in \\mathbb{T}^2,\\ p\\in B^2,\\ t\\in \\mathbb{T}, \\] with a strictly convex $H_0$, there exists a $\\rho$-dense orbit $(\\theta_{\\epsilon},p_{\\epsilon},t)(t)$ in $\\mathbb{T}^2 \\times B^2 \\times \\mathbb{T}$, namely, a $\\rho$-neighborhood of the orbit contains"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1150","kind":"arxiv","version":3},"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"}