{"paper":{"title":"Lifting mixing properties by Rokhlin cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Parreau, M. Lemanczyk","submitted_at":"2011-02-04T07:45:55Z","abstract_excerpt":"We study the problem of lifting various mixing properties from a base automorphism $T\\in {\\rm Aut}\\xbm$ to skew products of the form $\\tfs$, where $\\va:X\\to G$ is a cocycle with values in a locally compact Abelian group $G$, $\\cs=(S_g)_{g\\in G}$ is a measurable representation of $G$ in ${\\rm Aut}\\ycn$ and $\\tfs$ acts on the product space\n  $(X\\times Y,\\cb\\ot\\cc,\\mu\\ot\\nu)$ by $$\\tfs(x,y)=(Tx,S_{\\va(x)}(y)).$$ It is also shown that whenever $T$ is ergodic (mildly mixing, mixing) but $\\tfs$ is not ergodic (is not mildly mixing, not mixing), then on a non-trivial factor $\\ca\\subset\\cc$ of $\\cs$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0848","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"}