{"paper":{"title":"Bounding the length of iterated integrals of the first nonzero Melnikov function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Dmitry Novikov, Jessie Pontigo-Herrera, Laura Ortiz-Bobadilla, Pavao Mardesic","submitted_at":"2017-03-10T20:22:13Z","abstract_excerpt":"We consider small polynomial deformations of integrable systems of the form $dF=0$, $F\\in\\mathbb{C}[x,y]$ and the first nonzero term $M_\\mu$ of the displacement function $\\Delta(t,\\epsilon)=\\sum_{i=\\mu}M_i(t)\\epsilon^i$ along a cycle $\\gamma(t)\\in F^{-1}(t)$. It is known that $M_\\mu$ is an iterated integral of length at most $\\mu$. The bound $\\mu$ depends on the deformation of $dF$.\n  In this paper we give a universal bound for the length of the iterated integral expressing the first nonzero term $M_\\mu$ depending only on the topology of the unperturbed system $dF=0$. The result generalizes th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03837","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"}