{"paper":{"title":"On the non-equivalence of the Bernoulli and K properties in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Federico Rodriguez-Hertz, Kurt Vinhage","submitted_at":"2016-12-08T18:22:58Z","abstract_excerpt":"We study skew products where the base is a hyperbolic automorphism of $\\mathbb{T}^2$, the fiber is a smooth area preserving flow on $\\mathbb{T}^2$ with one fixed point (of high degeneracy) and the skewing function is a smooth non coboundary with non-zero integral. The fiber dynamics can be represented as a special flow over an irrational rotation and a roof function with one power singularity. We show that for a full measure set of rotations the corresponding skew product is $K$ and not Bernoulli. As a consequence we get a natural class of volume-preserving diffeomorphisms of $\\mathbb{T}^4$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02754","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"}