{"paper":{"title":"Bounded complexity, mean equicontinuity and discrete spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Paul Thouvenot, Jian Li, Leiye Xu, Wen Huang, Xiangdong Ye","submitted_at":"2018-06-08T06:12:22Z","abstract_excerpt":"We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric $d_n$, the max-mean metric $\\hat{d}_n$ and the mean metric $\\bar{d}_n$, both in topological dynamics and ergodic theory.\n  It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_n$ (resp. $\\hat{d}_n$) if and only if it is equicontinuous (resp. equicontinuous in the mean). However, we construct minimal systems which have bounded complexity with respect to $\\bar{d}_n$ but not equicontinuous in the mean.\n  It turns out that an invariant measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02980","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.02980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}