{"paper":{"title":"Sharkovskii order for non-wandering points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Moreira, M. Carvalho","submitted_at":"2011-07-20T11:31:46Z","abstract_excerpt":"For a map $f:I \\rightarrow I$, a point $x \\in I$ is periodic with period $p \\in \\mathbb{N}$ if $f^p(x)=x$ and $f^j(x)\\not=x$ for all $0<j<p$. When $f$ is continuous and $I$ is an interval, a theorem due to Sharkovskii (\\cite{BC}) states that there is an order in $\\mathbb{N}$, say $\\lhd$, such that, if $f$ has a periodic point of period $p$ and $p \\lhd q$, then $f$ also has a periodic point of period $q$. In this work, we will see how an extension of this order $\\lhd$ to an ultrapower of the integer numbers yields a Sharkovskii-type result for non-wandering points of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3945","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"}