{"paper":{"title":"Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Ilya Pavlyukevich, Navaratnam Sri Namachchivaya, Nishanth Lingala","submitted_at":"2015-10-29T21:42:32Z","abstract_excerpt":"The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\\varepsilon$. It is well known that, as $\\varepsilon \\to 0$, the measure of the set of initial conditions which lead to 'capture in a resonance zone' goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08919","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"}