{"paper":{"title":"Ratner's property and mixing for special flows over two-dimensional rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K. Fraczek, M. Lemanczyk","submitted_at":"2010-02-13T22:10:20Z","abstract_excerpt":"We consider special flows over two-dimensional rotations by $(\\alpha,\\beta)$ on $\\T^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition $\\int_{\\T^2}f_x(x,y)\\,dx\\,dy\\neq 0\\neq \\int_{\\T^2}f_y(x,y)\\,dx\\,dy.$ Such flows are shown to be always weakly mixing and never partially rigid. For an uncountable set of $(\\alpha,\\beta)$ with both $\\alpha$ and $\\beta$ of unbounded partial quotients the strong mixing property is proved to hold. It is also proved that while specifying to a subclass of roof functions and to ergodic rotations for which $\\alpha$ and $\\beta$ are of bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2734","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"}