{"paper":{"title":"Topological transivity and mixing of the composition operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benito Pires, Udayan B. Darji","submitted_at":"2016-10-04T06:46:04Z","abstract_excerpt":"Let $X=(X,\\mathcal{B},\\mu)$ be a $\\sigma$-finite measure space and \\mbox{$f:X\\to X$} be a measurable transformation such that the composition operator $T_f:\\varphi\\mapsto \\varphi\\circ f$ is a bounded linear operator acting on $L^p(X,\\mathcal{B},\\mu)$, $1\\le p<\\infty$.\n  We provide a necessary and sufficient condition on $f$ for $T_f$ to be topologically transitive or topologically mixing.\n  We also characterize the topological dynamics of composition operators induced by weighted shifts, non-singular odometers and inner functions.\n  The results provided in this article hold for composition ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00863","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"}