{"paper":{"title":"Iterates of dynamical systems on compact metrizable countable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Uzc\\'ategui, S. Garc\\'ia-Ferreira, Y. Rodriguez-L\\'opez","submitted_at":"2014-04-26T21:29:50Z","abstract_excerpt":"Given a dynamical system $(X,f)$, we let $E(X,f)$ denote its Ellis semigroup and $E(X,f)^* = E(X,f) \\setminus \\{f^n : n \\in \\mathbb{N}\\}$. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We show that if $(X,f)$ is a dynamical system such that $X$ is a compact metric countable space and every accumulation point $X'$ is periodic, then either each function of $E(X,f)^*$ is continuous or each function of $E(X,f)^*$ is discontinuous. We describe an example of a dynamical system $(X,f)$ where $X$ is a compact metric countable space, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6686","kind":"arxiv","version":4},"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"}