{"paper":{"title":"Higher order almost automorphy, recurrence sets and the regionally proximal relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Song Shao, Wen Huang, Xiangdong Ye","submitted_at":"2011-10-30T10:42:25Z","abstract_excerpt":"In this paper, $d$-step almost automorphic systems are studied for $d\\in\\N$, which are the generalization of the classical almost automorphic ones.\n  For a minimal topological dynamical system $(X,T)$ it is shown that the condition $x\\in X$ is $d$-step almost automorphic can be characterized via various subsets of $\\Z$ including the dual sets of $d$-step Poincar\\'e and Birkhoff recurrence sets, and Nil$_d$ Bohr$_0$-sets by considering $N(x,V)=\\{n\\in\\Z: T^nx\\in V\\}$, where $V$ is an arbitrary neighborhood of $x$. Moreover, it turns out that the condition $(x,y)\\in X\\times X$ is regionally proxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6599","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"}