{"paper":{"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michael Dellnitz, P\\'eter Koltai, Raphael Gerlach","submitted_at":"2019-02-23T18:34:15Z","abstract_excerpt":"Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the original set. In order to additionally reveal their geometry we use diffusion mapst o find intrinsic coordinates. We illustrate our results on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky equation, as well as for the attractor of the Mackey-Glass delay differential equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08824","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"}