{"paper":{"title":"Quantifying the role of folding in nonautonomous flows: the unsteady Double-Gyre","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Erik Bollt, K.G.D. Sulalitha Priyankara, Sanjeeva Balasuriya","submitted_at":"2017-01-24T22:20:42Z","abstract_excerpt":"We analyze chaos in the well-known nonautonomous Double-Gyre system. A key focus is on folding, which is possibly the less-studied aspect of the \"stretching + folding = chaos\" mantra of chaotic dynamics. Despite the Double-Gyre not having the classical homoclinic structure for the usage of the Smale-Birkhoff theorem to establish chaos, we use the concept of folding to prove the existence of an embedded horseshoe-map. We also show how curvature of manifolds can be used to identify fold points in the Double-Gyre. This method is applicable to general nonautonomous flows in two dimensions, defined"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07094","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"}