{"paper":{"title":"Set-oriented numerical computation of rotation sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kathrin Padberg-Gehle, Katja Polotzek, Tobias J\\\"ager","submitted_at":"2017-02-20T22:03:47Z","abstract_excerpt":"We establish a set-oriented algorithm for the numerical approximation of the rotation set of homeomorphisms of the two-torus homotopic to the identity. A theoretical background is given by the concept of {\\epsilon}-rotation sets. These are obtained by replacing orbits with {\\epsilon}-pseudo-orbits in the definition of the Misiurewicz-Ziemian rotation set and are shown to converge to the latter as {\\epsilon} decreases to zero. Based on this result, we prove the convergence of the numerical approximations as precision and iteration time tend to infinity. Further, we provide analytic error estima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06190","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"}