{"paper":{"title":"Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Korepanov, I. Melbourne, Z. Kosloff","submitted_at":"2015-09-22T20:31:41Z","abstract_excerpt":"We consider families of fast-slow skew product maps of the form \\begin{align*} x_{n+1} = x_n+\\epsilon a(x_n,y_n,\\epsilon), \\quad y_{n+1} = T_\\epsilon y_n, \\end{align*} where $T_\\epsilon$ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables $x$ as $\\epsilon\\to0$. Similar results are obtained also for continuous time systems \\begin{align*} \\dot x = \\epsilon a(x,y,\\epsilon), \\quad \\dot y = g_\\epsilon(y). \\end{align*} Our results include cases where the family of fast dynamical systems consists of intermittent maps, unimodal maps (along the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06772","kind":"arxiv","version":3},"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"}