{"paper":{"title":"The anisotropic oscillator on the two-dimensional 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":"Angel Ballesteros, Fabio Musso, Francisco J. Herranz","submitted_at":"2012-06-30T10:13:27Z","abstract_excerpt":"An integrable generalization on the two-dimensional sphere S^2 and the hyperbolic plane H^2 of the Euclidean anisotropic oscillator Hamiltonian with \"centrifugal\" terms given by $H=1/2(p_1^2+p_2^2)+ \\delta q_1^2+(\\delta + \\Omega)q_2^2 +\\frac{\\lambda_1}{q_1^2}+\\frac{\\lambda_2}{q_2^2}$ is presented. The resulting generalized Hamiltonian H_\\kappa\\ depends explicitly on the constant Gaussian curvature \\kappa\\ of the underlying space, in such a way that all the results here presented hold simultaneously for S^2 (\\kappa>0), H^2 (\\kappa<0) and E^2 (\\kappa=0). Moreover, H_\\kappa\\ is explicitly shown t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0071","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"}