Devaney chaos of a set-valued map and its inverse limit

Yingcui Zhao, Lidong Wang and Nan Wang

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

Abstract: We study relationships between a set-valued map and its inverse limit about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. We show that periodic point set of a set-valued map is dense if and only if periodic point set of the inverse limit with the set-valued map is dense. Sensitivity of a set-valued map and its inverse limit are independent of each other. If the inverse limit with the set-valued map is chaotic in the sense of Devaney (respectively, transitive), then the set-valued map is chaotic in the sense of Devaney (respectively, transitive).

Keywords: Transitivity; Sensitivity; Devaney chaos; Set-valued maps; Generalized inverse limits (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923003557

DOI: 10.1016/j.chaos.2023.113454

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