{"paper":{"title":"On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Congping Lin, Nigel P. Byott, Yiwei Zhang","submitted_at":"2014-05-02T19:29:23Z","abstract_excerpt":"For an integer $m \\geq 2$, let $\\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\\pm m$ on each element of $\\mathcal{P}_m$. We investigate the effect on mixing properties when $f \\in \\mathcal{F}_m$ is composed with the interval exchange map given by a permutation $\\sigma \\in S_N$ interchanging the $N$ subintervals of $\\mathcal{P}_N$. This extends the work in a previous paper [N.P. Byott, M. Holland and Y. Zhang, DCDS, {\\bf 33}, (2013) 3365--3390], where we considered o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0481","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"}