{"paper":{"title":"On the mixing properties of piecewise expanding maps under composition with permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.DS","authors_text":"Mark Holland, Nigel P. Byott, Yiwei Zhang","submitted_at":"2012-03-22T23:05:16Z","abstract_excerpt":"We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal subintervals and $f$ is composed with a permutation of these. The case of the stretch-and-fold map $f(x)=mx \\bmod 1$ for integers $m \\geq 2$ is examined in detail. We give a combinatorial description of those permutations $\\sigma$ for which $\\sigma \\circ f$ is still (topologically) mixing, and show that the proportion of such permutations tends to $1$ as $N \\to \\infty$. We then investigate the mixing rate of $\\sigma \\circ f$ (as measured by the modulus of the second "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5145","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"}