{"paper":{"title":"Domains of analyticity for response solutions in strongly dissipative forced systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guido Gentile, Livia Corsi, Roberto Feola","submitted_at":"2012-10-15T12:22:09Z","abstract_excerpt":"We study the ordinary differential equation $\\varepsilon\\ddot x + \\dot x + \\varepsilon g(x) = \\e f(\\omega t)$, where $g$ and $f$ are real-analytic functions, with $f$ quasi-periodic in $t$ with frequency vector $\\omega$. If $c_{0} \\in \\mathbb{R}$ is such that $g(c_0)$ equals the average of $f$ and $g'(c_0)\\neq0$, under very mild assumptions on $\\omega$ there exists a quasi-periodic solution close to $c_0$. We show that such a solution depends analytically on $\\varepsilon$ in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3998","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"}