{"paper":{"title":"Mean dimension of $\\mathbb{Z}^k$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Elon Lindenstrauss, Masaki Tsukamoto, Yonatan Gutman","submitted_at":"2015-10-06T14:52:03Z","abstract_excerpt":"Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a $\\mathbb{Z}^k$-action on a compact metric space $X$, we study the following three problems closely related to mean dimension.\n  (1) When is $X$ isomorphic to the inverse limit of finite entropy systems?\n  (2) Suppose the topological entropy $h_{\\mathrm{top}}(X)$ is infinite. How much topological entropy can be detected if one considers $X$ only up to a given level of accuracy? How fast does this amount of entropy grow as the level of resolution be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01605","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"}