{"paper":{"title":"Arnold diffusion for a complete family of perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Amadeu Delshams, Rodrigo G. Schaefer","submitted_at":"2016-08-30T11:42:35Z","abstract_excerpt":"In this work we illustrate the Arnold diffusion in a concrete example---the \\emph{a priori} unstable Hamiltonian system of $2+1/2$ degrees of freedom $H(p,q,I,\\varphi,s) = p^{2}/2+\\cos q -1 +I^{2}/2 + h(q,\\varphi,s;\\varepsilon)$---proving that for \\emph{any} small periodic perturbation of the form $h(q,\\varphi,s;\\varepsilon) = \\varepsilon\\cos q\\left( a_{00} + a_{10}\\cos\\varphi + a_{01}\\cos s \\right)$ ($a_{10}a_{01} \\neq 0$) there is global instability for the action. For the proof we apply a geometrical mechanism based in the so-called Scattering map.\n  This work has the following structure: I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08408","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"}