{"paper":{"title":"The 1:1 resonance in Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Heinz Hanssmann, Igor Hoveijn","submitted_at":"2017-04-10T07:09:32Z","abstract_excerpt":"Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the frequencies pass through a resonance. These bifurcations are well understood for most resonances k:l, but not the semisimple cases 1:1 and 1:-1. A two-degree-of-freedom Hamiltonian system can be approximated to any order by an integrable approximation. The reason is that the normal form of a Hamiltonian system has an additional integral due to the normal form symmetr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02733","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"}