{"paper":{"title":"On the invariant manifolds of the fixed point of a second order nonlinear difference equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mehmet Turan","submitted_at":"2018-06-12T15:29:31Z","abstract_excerpt":"This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equation $x_{n+1} = \\alpha + \\beta x_{n-1}+x_{n-1}/x_{n},$ where $\\alpha>0,$ $0\\leqslant \\beta <1$ and the initial conditions $x_{-1}$ and $x_0$ are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04607","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"}