{"paper":{"title":"Integrability of the Hide--Skeldon--Acheson dynamo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Adam Mahdi, Claudia Valls","submitted_at":"2014-04-03T22:23:11Z","abstract_excerpt":"In this work we consider the Hide-Skeldon-Acheson dynamo model \\[ \\dot x=x(y-1)-\\beta z, \\quad \\dot y =\\alpha(1-x^2)-\\kappa y, \\quad \\dot z =x-\\lambda z, \\] where $\\alpha,\\beta,\\kappa$ and $\\lambda$ are parameters.\n  We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. Provided $\\alpha \\ne 0$ we identify the values of the parameters of this model, for which it admits a first integral. Also, as corollary of our main results we get that for $\\alpha, \\beta, \\kappa \\ne 0$ the dynamo model doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1110","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"}