{"paper":{"title":"A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"J. A. Vallejo, M. Avenda\\~no-Camacho, Yu. Vorobjev","submitted_at":"2013-01-15T07:10:13Z","abstract_excerpt":"We study the determination of the second-order normal form for perturbed Hamiltonians $H_{\\epsilon}=H_0 +\\epsilon H_1 +\\frac{\\epsilon^2}{2} H_2$, relative to the periodic flow of the unperturbed Hamiltonian $H_0$. The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H\\'enon-Heiles and the elastic pendulum Hamiltonians."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3244","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"}