{"paper":{"title":"Sensitivity, proximal extension and higher order almost automorphy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tao Yu, Xiangdong Ye","submitted_at":"2016-05-04T00:17:20Z","abstract_excerpt":"Let $(X,T)$ be a topological dynamical system, and $\\mathcal{F}$ be a family of subsets of $\\mathbb{Z}_+$. $(X,T)$ is strongly $\\mathcal{F}$-sensitive, if there is $\\delta>0$ such that for each non-empty open subset $U$, there are $x,y\\in U$ with $\\{n\\in\\mathbb{Z}_+: d(T^nx,T^ny)>\\delta\\}\\in\\mathcal{F}$. Let $\\mathcal{F}_t$ (resp. $\\mathcal{F}_{ip}$, $\\mathcal{F}_{fip}$) be consisting of thick sets (resp. IP-sets, subsets containing arbitrarily long finite IP-sets).\n  The following Auslander-Yorke's type dichotomy theorems are obtained: (1) a minimal system is either strongly $\\mathcal{F}_{fip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01119","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"}