{"paper":{"title":"Instability of high dimensional Hamiltonian Systems: Multiple resonances do not impede diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Amadeu Delshams, Rafael de la Llave, Tere M. Seara","submitted_at":"2013-06-19T16:52:50Z","abstract_excerpt":"We consider models given by Hamiltonians of the form $$H(I,\\phi,p,q,t;\\epsilon) = h(I) + \\sum_{j = 1}^n \\pm(\\frac{1}{2} p_j^2 + V_j(q_j)) + \\epsilon Q(I,\\phi,p,q,t;\\epsilon)$$ where $I,\\phi$ are d-dimensional actions and angles, $p,q$ are n-dimensional real conjugated variables, and $t$ is an angle. These are higher dimensional analogues, both in the center and hyperbolic directions, of the models studied in previous papers by the athors. All these models present the large gap problem.\n  We show that, for $\\epsilon$ small enough, under regularity and explicit non-degeneracy conditions on the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4614","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"}