{"paper":{"title":"Structure-Preserving Flows of Symplectic Matrix Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Shih-Feng Shieh, Wen-Wei Lin, Yueh-Cheng Kuo","submitted_at":"2014-12-02T05:51:18Z","abstract_excerpt":"We construct a nonlinear differential equation of matrix pairs $(\\mathcal{M}(t),\\mathcal{L}(t))$ that is invariant (the \\textbf{Structure-Preserving Property}) in the class of symplectic matrix pairs \\begin{align*} \\mathbb{S}_{\\mathcal{S}_1,\\mathcal{S}_2}=\\left\\{\\left(\\mathcal{M},\\mathcal{L}\\right)| \\ \\mathcal{M}=\\left[% \\begin{array}{cc}\n  X_{12} & 0\n  X_{22} & I \\end{array}% \\right]\\mathcal{S}_2, \\mathcal{L}=\\left[% \\begin{array}{cc}\n  I & X_{11}\n  0 & X_{21} \\end{array}% \\right]\\mathcal{S}_1\\right.\\nonumber  \\left. \\text{ and }X=\\left[% \\begin{array}{cc}\n  X_{11} & X_{12}\n  X_{21} & X_{22} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0786","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"}