{"paper":{"title":"A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marlies Gerber, Philipp Kunde","submitted_at":"2018-03-05T21:12:03Z","abstract_excerpt":"Let $M$ be a smooth compact connected manifold of dimension $d\\geq 2$, possibly with boundary, that admits a smooth effective $\\mathbb{T}^2$-action $\\mathcal{S}=\\left\\{S_{\\alpha,\\beta}\\right\\}_{(\\alpha,\\beta) \\in \\mathbb{T}^2}$ preserving a smooth volume $\\nu$, and let $\\mathcal{B}$ be the $C^{\\infty}$ closure of $\\left\\{h \\circ S_{\\alpha,\\beta} \\circ h^{-1} \\;:\\;h \\in \\text{Diff}^{\\infty}\\left(M,\\nu\\right), (\\alpha,\\beta) \\in \\mathbb{T}^2\\right\\}$. We construct a $C^{\\infty}$ diffeomorphism $T \\in \\mathcal{B}$ with topological entropy $0$ such that $T \\times T$ is loosely Bernoulli. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01926","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"}