{"paper":{"title":"On two superintegrable nonlinear oscillators in N dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alberto Enciso, Angel Ballesteros, Danilo Riglioni, Francisco J. Herranz, Orlando Ragnisco","submitted_at":"2010-10-16T14:33:48Z","abstract_excerpt":"We consider the classical superintegrable Hamiltonian system given by $H=T+U={p^2}/{2(1+\\lambda q^2)}+{{\\omega}^2 q^2}/{2(1+\\lambda q^2)}$, where U is known to be the \"intrinsic\" oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term T and parametrized by {\\lambda}. We show that H is Stackel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for H. Furthermore, we analyze in terms of {\\lambda} the three different underlying manifolds whose geodesic motion is provided by T. As a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3358","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"}