{"paper":{"title":"M\\\"obius disjointness for non-uniquely ergodic skew products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Zhiren Wang","submitted_at":"2016-08-09T05:54:21Z","abstract_excerpt":"For $\\tau>2$, let $T$ be a $C^\\tau$ skew product map of the form $(x+\\alpha,y+h(x))$ on $\\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the M\\\"{o}bius sequence. This in particular implies that any non-uniquely ergodic $C^\\tau$ skew product map on $\\mathbb T^2$ has a finite index factor that is disjoint to the M\\\"{o}bius sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02697","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"}