{"paper":{"title":"Li-Yorke chaos on fuzzy dynamical systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antoni L\\'opez-Mart\\'inez, Illych \\'Alvarez","submitted_at":"2025-10-23T05:46:43Z","abstract_excerpt":"Given a dynamical system $(X,f)$ we investigate how several variants of Li-Yorke chaos behave with respect to the extended systems $(\\mathcal{K}(X),\\overline{f})$ and $(\\mathcal{F}(X),\\hat{f})$, where $\\overline{f}$ is the hyperextension of $f$ acting on the space $\\mathcal{K}(X)$ of non-empty compact subsets of $X$, and where $\\hat{f}$ denotes the Zadeh extension of $f$ acting on the space $\\mathcal{F}(X)$ of normal fuzzy subsets of $X$. We first prove that the main variants of Li-Yorke chaos transfer from $(X,f)$ to $(\\mathcal{K}(X),\\overline{f})$ and from $(\\mathcal{K}(X),\\overline{f})$ to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.20240","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.20240/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}