{"paper":{"title":"Singularities of integrable Hamiltonian systems: a criterion for non-degeneracy, with an application to the Manakov top","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.SG"],"primary_cat":"nlin.SI","authors_text":"Dmitry Tonkonog","submitted_at":"2010-09-04T19:38:53Z","abstract_excerpt":"Let (M,\\omega) be a symplectic 2n-manifold and h_1,...,h_n be functionally independent commuting functions on M. We present a geometric criterion for a singular point P\\in M (i.e. such that {dh_i(P)}_{i=1}^n are linearly dependent) to be non-degenerate in the sence of Vey-Eliasson.\n  Then we apply Fomenko's theory to study the neighborhood U of the singular Liouville fiber containing saddle-saddle singularities of the Manakov top. Namely, we describe the singular Liouville foliation on U and the `Bohr-Sommerfeld' lattices on the momentum map image of U. A relation with the quantum Manakov top "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0863","kind":"arxiv","version":3},"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"}