{"paper":{"title":"Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Alireza Hadjighasem, George Haller, Mohammad Farazmand","submitted_at":"2013-02-07T12:49:30Z","abstract_excerpt":"We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy-Green strain tensor computed from the flow map of the forced mechanical system. This approach enables the finite-time visualization of generalized stable and unstable manifolds, attractors and generalized KAM curves under arbitrary forcing, when Poincare maps are not available. We illus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1732","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"}