{"paper":{"title":"M\\\"obius disjointness along ergodic sequences for uniquely ergodic actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","submitted_at":"2017-03-07T12:16:23Z","abstract_excerpt":"We show that there are an irrational rotation $Tx=x+\\alpha$ on the circle $\\mathbb{T}$ and a continuous $\\varphi\\colon\\mathbb{T}\\to\\mathbb{R}$ such that for each (continuous) uniquely ergodic flow $\\mathcal{S}=(S_t)_{t\\in\\mathbb{R}}$ acting on a compact metric space $Y$, the automorphism $T_{\\varphi,\\mathcal{S}}$ acting on $(X\\times Y,\\mu\\otimes\\nu)$ by the formula $T_{\\varphi,\\mathcal{S}}(x,y)=(Tx,S_{\\varphi(x)}(y))$, where $\\mu$ stands for Lebesgue measure on $\\mathbb{T}$ and $\\nu$ denotes the unique $\\mathcal{S}$-invariant measure, has the property of asymptotically orthogonal powers. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02347","kind":"arxiv","version":1},"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"}