{"paper":{"title":"Mean Dimension & Jaworski-type Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yonatan Gutman","submitted_at":"2012-08-26T20:25:56Z","abstract_excerpt":"According to the celebrated Jaworski Theorem, a finite dimensional aperiodic dynamical system $(X,T)$ embeds in the $1$-dimensional cubical shift $([0,1]^{\\mathbb{Z}},shift)$. If $X$ admits periodic points (still assuming $\\dim(X)<\\infty$) then we show in this paper that periodic dimension $perdim(X,T)<\\frac{d}{2}$ implies that $(X,T)$ embeds in the $d$-dimensional cubical shift $(([0,1]^{d})^{\\mathbb{Z}},shift)$. This verifies a conjecture by Lindenstrauss and Tsukamoto for finite dimensional systems. Moreover for an infinite dimensional dynamical system, with the same periodic dimension assu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5248","kind":"arxiv","version":6},"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"}