{"paper":{"title":"On aperiodicity and hypercyclic weighted translation operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kui-Yo Chen","submitted_at":"2017-01-13T09:30:14Z","abstract_excerpt":"We give several equivalent characterization of aperiodicity of an element on locally compact group $G$, and give an intuition for \"How strong does the aperiodicity of an element affect the existence of hypercyclic weighted translation operators?\". In fact, if $a$ is an aperiodic element in $G$, then there exists a mixing, chaotic and frequently hypercyclic weighted translation $T_{a,w}$ on $L^p(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03604","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"}