{"paper":{"title":"The degenerate C. Neumann system I: symmetry reduction and convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG","nlin.SI"],"primary_cat":"math.DS","authors_text":"Heinz Han{\\ss}mann, Holger R. Dullin","submitted_at":"2012-05-08T21:40:24Z","abstract_excerpt":"The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\\sigma equal eigenvalues gives rise to an O(m_\\sigma)-symmetry in configuration space. The combined symmetry group G is a direct product of l+1 such factors, and its cotangent lift has an Ad^*-equivariant Momentum mapping. Regular reduction leads to the Rosochatius system on S^l, which has the same form as the Neumann system albeit for an additional effective potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1834","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"}