{"paper":{"title":"On bifurcation of eigenvalues along convex symplectic paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jian Wang, Yiming Long, Yinshan Chang","submitted_at":"2017-10-22T13:57:58Z","abstract_excerpt":"We consider a continuously differentiable curve $t\\mapsto \\gamma(t)$ in the space of $2n\\times 2n$ real symplectic matrices, which is the solution of the following ODE:\n  $\\frac{\\mathrm{d}\\gamma}{\\mathrm{d}t}(t)=J_{2n}A(t)\\gamma(t), \\gamma(0)\\in\\operatorname{Sp}(2n,\\mathbb{R})$,\n  where $J=J_{2n}\\overset{\\text{def}}{=}\\begin{bmatrix}0 & \\operatorname{Id}_n\\\\-\\operatorname{Id}_n & 0\\end{bmatrix}$ and $A:t\\mapsto A(t)$ is a continuous in the space of $2n\\times2n$ real matrices which are symmetric. Under certain convexity assumption (which includes the particular case that $A(t)$ is strictly posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07940","kind":"arxiv","version":2},"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"}