{"paper":{"title":"An integrable Henon-Heiles system on the sphere and the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Alfonso Blasco, Angel Ballesteros, Fabio Musso, Francisco J. Herranz","submitted_at":"2014-11-07T21:11:01Z","abstract_excerpt":"We construct a constant curvature analogue on the two-dimensional sphere ${\\mathbf S}^2$ and the hyperbolic space ${\\mathbf H}^2$ of the integrable H\\'enon-Heiles Hamiltonian $\\mathcal{H}$ given by $$ \\mathcal{H}=\\dfrac{1}{2}(p_{1}^{2}+p_{2}^{2})+ \\Omega \\left( q_{1}^{2}+ 4 q_{2}^{2}\\right) +\\alpha \\left( q_{1}^{2}q_{2}+2 q_{2}^{3}\\right) , $$ where $\\Omega$ and $\\alpha$ are real constants. The curved integrable Hamiltonian $\\mathcal{H}_\\kappa$ so obtained depends on a parameter $\\kappa$ which is just the curvature of the underlying space, and is such that the Euclidean H\\'enon-Heiles system $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2033","kind":"arxiv","version":2},"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"}