{"paper":{"title":"The continuous transition of Hamiltonian vector fields through manifolds of constant curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.DS","authors_text":"Florin Diacu, Jedrzej Sniatycki, Slim Ibrahim","submitted_at":"2015-10-21T16:26:05Z","abstract_excerpt":"We ask whether Hamiltonian vector fields defined on spaces of constant Gaussian curvature $\\kappa$ (spheres, for $\\kappa>0$, and hyperbolic spheres, for $\\kappa<0$), pass continuously through the value $\\kappa=0$ if the potential functions $U_\\kappa, \\kappa\\in\\mathbb R$, that define them satisfy the property $\\lim_{\\kappa\\to 0}U_\\kappa=U_0$, where $U_0$ corresponds to the Euclidean case. We prove that the answer to this question is positive, both in the 2- and 3-dimensional cases, which are of physical interest, and then apply our conclusions to the gravitational $N$-body problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06327","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"}