{"paper":{"title":"For graph maps, one scrambled pair implies Li-Yorke chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"L'ubom\\'ir Snoha, Sylvie Ruette","submitted_at":"2012-05-17T09:00:24Z","abstract_excerpt":"For a dynamical system $(X,f)$, $X$ being a compact metric space with metric $d$ and $f$ being a continuous map $X\\to X$, a set $S\\subseteq X$ is scrambled if every pair $(x,y)$ of distinct points in $S$ is scrambled, i.e., $\\liminf_{n\\to+\\infty}d(f^n(x),f^n(y))=0$ and $\\limsup_{n\\to+\\infty}d(f^n(x),f^n(y))>0$. The system $(X,f)$ is Li-Yorke chaotic if it has an uncountable scrambled set. It is known that, for interval and circle maps, the existence of a scrambled pair implies Li-Yorke chaos, in fact the existence of a Cantor scrambled set. We prove that the same result holds for graph maps. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3882","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"}