{"paper":{"title":"Universal Curves in the Center Problem for Abel Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Brudnyi","submitted_at":"2014-05-20T00:42:01Z","abstract_excerpt":"We study the center problem for the class $\\mathcal E_\\Gamma$ of Abel differential equations $\\frac{dv}{dt}=a_1 v^2+a_2 v^3$, $a_1,a_2\\in L^\\infty ([0,T])$, such that images of Lipschitz paths $\\tilde A:=\\bigl(\\int_0^\\cdot a_1(s)ds, \\int_0^\\cdot a_2(s)ds\\bigr): [0,T]\\rightarrow\\mathbb R^2$ belong to a fixed compact rectifiable curve $\\Gamma$. Such a curve is called universal if whenever an equation in $\\mathcal E_\\Gamma$ has center on $[0,T]$, this center must be universal, i.e. all iterated integrals in coefficients $a_1, a_2$ of this equation must vanish. We investigate some basic properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4924","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"}