{"paper":{"title":"Darboux theory of integrability for real polynomial vector fields on $\\sss^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adrian C. Murza, Jaume Llibre","submitted_at":"2017-02-17T19:00:26Z","abstract_excerpt":"This is a survey on the Darboux theory of integrability for polynomial vector fields, first in $\\R^n$ and second in the $n$-dimensional sphere $\\sss^n$. We also provide new results about the maximum number of parallels and meridians that a polynomial vector field $\\X$ on $\\sss^n$ can have in function of its degree. These results in some sense extend the known result on the maximum number of hyperplanes that a polynomial vector field $\\Y$ in $\\R^n$ can have in function of the degree of $\\Y$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05495","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"}