{"paper":{"title":"Sensitive dependence and transitivity of fuzzified dynamical systems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guanrong Chen, Xinxing Wu, Xiong Wang","submitted_at":"2016-05-18T12:47:22Z","abstract_excerpt":"This paper proves that a set-valued dynamical system is sensitively dependent on initial conditions (resp., $\\mathscr{F}$-sensitive, multi-sensitive) if and only if its $g$-fuzzification is sensitively dependent on initial conditions (resp., $\\mathscr{F}$-sensitive, multi-sensitive), where $\\mathscr{F}$ is a Furstenberg family. As an application, it is shown that there exists a sensitive dynamical system whose $g$-fuzzification does not have such sensitive dependence for any $g$ in a certain domain. Moreover, a sufficient condition ensuring that the $g$-fuzzification of every nontrivial dynami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06374","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"}