{"paper":{"title":"Searching chaotic saddles in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"nlin.CD","authors_text":"E.G. Altmann, J.C. Leitao, M. Sala","submitted_at":"2016-10-18T06:37:15Z","abstract_excerpt":"We propose new methods to numerically approximate non-attracting sets governing transiently-chaotic systems. Trajectories starting in a vicinity $\\Omega$ of these sets escape $\\Omega$ in a finite time $\\tau$ and the problem is to find initial conditions ${\\bf x} \\in \\Omega$ with increasingly large $\\tau= \\tau({\\bf x})$. We search points ${\\bf x}'$ with $\\tau({\\bf x}')>\\tau({\\bf x})$ in a {\\it search domain} in $\\Omega$. Our first method considers a search domain with size that decreases exponentially in $\\tau$, with an exponent proportional to the largest Lyapunov exponent $\\lambda_1$. Our sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05450","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"}