{"paper":{"title":"Convergent series for quasi-periodically forced strongly dissipative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Guido Gentile, Livia Corsi, Roberto Feola","submitted_at":"2012-11-09T13:34:05Z","abstract_excerpt":"We study the ordinary differential equation ${\\varepsilon}\\ddot x+\\dot x + {\\varepsilon} g(x) = {\\varepsilon} f(\\omega t)$, with $f$ and $g$ analytic and $f$ quasi-periodic in $t$ with frequency vector $\\omega\\in R^{d}$. We show that if there exists $c_0\\in R$ such that $g(c_0)$ equals the average of $f$ and the first non-zero derivative of $g$ at $c_0$ is of odd order $n$, then, for ${\\varepsilon}$ small enough and under very mild Diophantine conditions on $\\omega$, there exists a quasi-periodic solution close to $c_0$, with the same frequency vector as $f$. In particular if $f$ is a trigonom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2125","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"}