{"paper":{"title":"Recurrence in the dynamical system $(X,\\langle T_s\\rangle_{s\\in S})$ and ideals of $\\beta S$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dona Strauss, Luca Q. Zamboni, Neil Hindman","submitted_at":"2016-08-19T08:47:19Z","abstract_excerpt":"A {\\it dynamical system\\/} is a pair $(X,\\langle T_s\\rangle_{s\\in S})$, where $X$ is a compact Hausdorff space, $S$ is a semigroup, for each $s\\in S$, $T_s$ is a continuous function from $X$ to $X$, and for all $s,t\\in S$, $T_s\\circ T_t=T_{st}$. Given a point $p\\in\\beta S$, the Stone-\\v Cech compactification of the discrete space $S$, $T_p:X\\to X$ is defined by, for $x\\in X$, $\\displaystyle T_p(x)=p{-}\\!\\lim_{s\\in S}T_s(x)$. We let $\\beta S$ have the operation extending the operation of $S$ such that $\\beta S$ is a right topological semigroup and multiplication on the left by any point of $S$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05535","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"}