{"paper":{"title":"Chains of compact cylinders for cusp-generic nearly integrable convex systems on $\\mathbb{A}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Pierre Marco","submitted_at":"2016-02-07T18:10:45Z","abstract_excerpt":"This paper is the first of a series of three dedicated to a proof of the Arnold diffusion conjecture for perturbations of {convex} integrable Hamiltonian systems on $\\mathbb{A}^3=\\mathbb{T}^3\\times \\mathbb{R}^3$.\n  We consider systems of the form $H(\\theta,r)=h(r)+f(\\theta,r)$, where $h$ is a $C^\\kappa$ strictly convex and superlinear function on $\\mathbb{R}^3$ and $f\\in C^\\kappa(\\mathbb{A}^3)$, $\\kappa\\geq2$. Given $e>\\textrm{{Min}}\\,h$ and a finite family of arbitrary open sets $O_i$ in $\\mathbb{R}^3$ intersecting $h^{-1}(e)$, a diffusion orbit associated with these data is an orbit of $H$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02399","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"}