{"paper":{"title":"Various aspects of differential equations having a complete set of independent first integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"N. Sadovskaia, R. Ram\\'irez","submitted_at":"2011-06-13T21:11:07Z","abstract_excerpt":"In this paper we study the differential equations in $D\\subseteq \\R^{2N}$ having a complete set of independent first integrals. In particular we study the case when the first integrals are \\[f_\\nu=(Ax_\\nu+By_\\nu)^2+\\displaystyle\\sum_{j=1}^{N}\\dfrac{(x_\\nu y_j-x_jy_\\nu)^2}{a_\\nu-a_j},\\]for $\\nu=1,...,N,$ where $A,B$ and $a_1<a_2...<a_N$ are constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2563","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"}