{"paper":{"title":"A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.CA"],"primary_cat":"math.DS","authors_text":"Ainhoa Aparicio, Jacques-Arthur Weil","submitted_at":"2012-06-27T17:38:40Z","abstract_excerpt":"Let $\\mathbf{k}$ be a differential field and let $[A]\\,:\\,Y'=A\\,Y$ be a linear differential system where $A\\in\\mathrm{Mat}(n\\,,\\,\\mathbf{k})$. We say that $A$ is in a reduced form if $A\\in\\mathfrak{g}(\\bar{\\mathbf{k}})$ where $\\mathfrak{g}$ is the Lie algebra of $[A]$ and $\\bar{\\mathbf{k}}$ denotes the algebraic closure of $\\mathbf{k}$. We owe the existence of such reduced forms to a result due to Kolchin and Kovacic \\cite{Ko71a}. This paper is devoted to the study of reduced forms, of (higher order) variational equations along a particular solution of a complex analytical hamiltonian system $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6345","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"}