{"paper":{"title":"The embedding problem in topological dynamics and Takens' theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabor Szabo, Yixiao Qiao, Yonatan Gutman","submitted_at":"2017-08-20T14:28:07Z","abstract_excerpt":"We prove that every $\\mathbb{Z}^{k}$-action $(X,\\mathbb{Z}^{k},T)$ of mean dimension less than $D/2$ admitting a factor $(Y,\\mathbb{Z}^{k},S)$ of Rokhlin dimension not greater than $L$ embeds in $(([0,1]^{(L+1)D})^{\\mathbb{Z}^{k}}\\times Y,\\sigma\\times S)$, where $D\\in\\mathbb{N}$, $L\\in\\mathbb{N}\\cup\\{0\\}$ and $\\sigma$ is the shift on the Hilbert cube $([0,1]^{(L+1)D})^{\\mathbb{Z}^{k}}$; in particular, when $(Y,\\mathbb{Z}^{k},S)$ is an irrational $\\mathbb{Z}^{k}$-rotation on the $k$-torus, $(X,\\mathbb{Z}^{k},T)$ embeds in $(([0,1]^{2^kD+1})^{\\mathbb{Z}^k},\\sigma)$, which is compared to a previo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05972","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"}