{"paper":{"title":"Li-Yorke chaos for dendrite maps with zero topological entropy and $\\omega$-limit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ghassen Askri","submitted_at":"2015-06-23T06:14:09Z","abstract_excerpt":"Let $X$ be a dendrite  with  set of endpoints $E(X)$ closed  and let $f:~X \\to X$ be a continuous map with zero topological entropy.  Let $P(f)$ be the set of periodic points of $f$. We prove that if $L$ is an infinite $\\omega$-limit set of $f$ then $L\\cap P(f)\\subset E(X)^{\\prime}$, where $E(X)^{\\prime}$ is the set of all accumulations points of $E(X)$. Furthermore, if $E(X)$ is countable and $L$ is uncountable then $L\\cap P(f)=\\emptyset$. We also show  that if $E(X)^{\\prime}$ is finite then any uncountable $\\omega$-limit set of $f$ has a decomposition and as a consequence if $f$ has a Li-Yor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06872","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"}