{"paper":{"title":"Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.DS","authors_text":"Kaname Matsue","submitted_at":"2016-12-07T09:30:30Z","abstract_excerpt":"We provide a rigorous numerical computation method to validate tubular neighborhoods of normally hyperbolic slow manifolds with the explicit radii for the fast-slow system \\begin{equation*} \\begin{cases} x' = f(x,y,\\epsilon), and y' =\\epsilon g(x,y,\\epsilon). & \\end{cases} \\end{equation*} Our main focus is the validation of the continuous family of eigenpairs $\\{\\lambda_i(y;\\epsilon), u_i(y;\\epsilon)\\}_{i=1}^n$ of $f_x(h_\\epsilon(y),y,\\epsilon)$ over the slow manifold $S_\\epsilon = \\{x = h_\\epsilon(y)\\}$ admitting the graph representation. In order to obtain such a family, we apply the interva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02162","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"}