{"paper":{"title":"On the N-Extended Euler System I. Generalized Jacobi Elliptic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco Crespo, Francisco Javier Molero, Sebasti\\'an Ferrer","submitted_at":"2015-05-22T16:52:09Z","abstract_excerpt":"We study the integrable system of first order differential equations $\\omega_i(v)'=\\alpha_i\\,\\prod_{j\\neq i}\\omega_j(v)$, $(1\\!\\leq i, j\\leq\\! N)$ as an initial value problem, with real coefficients $\\alpha_i$ and initial conditions $\\omega_i(0)$. The analysis is based on its quadratic first integrals. For each dimension $N$, the system defines a family of functions, generically hyperelliptic functions. When $N=3$, this system generalizes the classic Euler system for the reduced flow of the free rigid body problem, thus we call it $N$-extended Euler system ($N$-EES). In this Part I the cases $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06142","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"}