{"paper":{"title":"Poisson and symplectic reductions of 4-DOF isotropic oscillators. The van der Waals system as benchmark","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco Crespo, Gema Mar\\'ia D\\'iaz-Toca, Mart\\'in Lara, Sebasti\\'an Ferrer","submitted_at":"2015-02-07T23:48:33Z","abstract_excerpt":"This paper is devoted to studying Hamiltonian oscillators in 1:1:1:1 resonance with symmetries, which include several models of perturbed Keplerian systems. Normal forms are computed in Poisson and symplectic formalisms, by mean of invariants and Lie-transforms respectively. The first procedure relies on the quadratic invariants associated to the symmetries, and is carried out using Gr\\\"obner bases. In the symplectic approach, hinging on the maximally superintegrable character of the isotropic oscillator, the normal form is computed {\\it a la} Delaunay, using a generalization of those variable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02196","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"}