{"paper":{"title":"Computational complexity of solving polynomial differential equations over unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amaury Pouly, Daniel S. Gra\\c{c}a","submitted_at":"2014-09-01T15:22:54Z","abstract_excerpt":"In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) $y^{\\prime}=p(y)$ over \\emph{unbounded time domains}, where $p$ is a vector of polynomials. Contrarily to the bounded (compact) time case, this problem has not been well-studied, apparently due to the \"intuition\" that it can always be reduced to the bounded case by using rescaling techniques. However, as we show in this paper, rescaling techniques do not seem to provide meaningful insights on the complexity of this problem, since the use of such techniques introduces a dependence on para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0451","kind":"arxiv","version":4},"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"}