{"paper":{"title":"Weakly mixing diffeomorphisms preserving a measurable Riemannian metric are dense in $\\mathcal{A}_{\\alpha}\\left(M\\right)$ for arbitrary Liouvillean number $\\alpha$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Philipp Kunde, Roland Gunesch","submitted_at":"2015-11-30T22:32:22Z","abstract_excerpt":"We show that on any smooth compact connected manifold of dimension $m\\geq 2$ admitting a smooth non-trivial circle action $\\mathcal{S} = \\left\\{S_t\\right\\}_{t \\in \\mathbb{R}}$, $S_{t+1}=S_t$, the set of weakly mixing $C^{\\infty}$-diffeomorphisms which preserve both a smooth volume $\\nu$ and a measurable Riemannian metric is dense in $\\mathcal{A}_{\\alpha} \\left(M\\right)= \\overline{ \\left\\{h \\circ S_{\\alpha} \\circ h^{-1} : h \\in \\text{Diff}^{\\infty}\\left(M, \\nu\\right) \\right\\}}^{C^{\\infty}}$ for every Liouvillean number $\\alpha$. The proof is based on a quantitative version of the Anosov-Katok-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00075","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"}