{"paper":{"title":"Eventual nonsensitivity and tame dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GN"],"primary_cat":"math.DS","authors_text":"Eli Glasner, Michael Megrelishvili","submitted_at":"2014-05-11T21:35:54Z","abstract_excerpt":"In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts $X \\subset \\{0,1\\}^{\\mathbb Z}$: for every infinite subset $L \\subseteq {\\mathbb Z}$ there exists an infinite subset $K \\subseteq L$ such that $\\pi_{K}(X)$ is a countable subset of $\\{0,1\\}^K$. The notion of eventual fragmentability is one of the properties we encounter which indicate some \"smallness\" of a family. We investigate a \"smallness hierarchy\" for families of continuous functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2588","kind":"arxiv","version":7},"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"}