{"paper":{"title":"Explicit Construction of First Integrals with Quasi-monomial Terms from the Painlev\\'{e} Series","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Christos Efthymiopoulos, Tassos Bountis, Thanos Manos","submitted_at":"2008-01-11T15:36:57Z","abstract_excerpt":"The Painlev\\'{e} and weak Painlev\\'{e} conjectures have been used widely to identify new integrable nonlinear dynamical systems. For a system which passes the Painlev\\'{e} test, the calculation of the integrals relies on a variety of methods which are independent from Painlev\\'{e} analysis. The present paper proposes an explicit algorithm to build first integrals of a dynamical system, expressed as `quasi-polynomial' functions, from the information provided solely by the Painlev\\'{e} - Laurent series solutions of a system of ODEs. Restrictions on the number and form of quasi-monomial terms app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1791","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"}