{"paper":{"title":"Equicontinuity of maps on dendrites","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Uzc\\'ategui, Javier Camargo, Michael Rinc\\'on","submitted_at":"2018-11-12T16:37:26Z","abstract_excerpt":"Given a dendrite $X$ and a continuous map $f\\colon X\\to X$, we show the following are equivalent: (i) $\\omega_f$ is continuous and $\\overline{\\mathrm{Per}(f)}=\\bigcap_{n\\in\\mathbb{N}}f^n(X)$; (ii) $\\omega(x,f)=\\Omega(x,f)$ for each $x\\in X$; and (iii) $f$ is equicontinuous. Furthermore, we present some examples illustrating our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04841","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"}