Geodesic
Shadowing for induced maps of hyperspaces
Leobardo Fernández 1   ; Chris Good 1
1 School of Mathematics University of Birmingham Birmingham, United Kingdom B15 2TT
Fundamenta Mathematicae, Tome 235 (2016) no. 3, pp. 277-286 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given a nonempty compact metric space $X$ and a continuous function $f:X \to X$, we study shadowing and $h$-shadowing for the induced maps on hyperspaces, particularly in symmetric products, $F_{n}(X)$, and the hyperspace $2^{X}$ of compact subsets of $X$. We prove that $f$ has shadowing [$h$-shadowing] if and only if $2^{f}$ has shadowing [$h$-shadowing].
DOI : 10.4064/fm136-2-2016
Keywords: given nonempty compact metric space continuous function study shadowing h shadowing induced maps hyperspaces particularly symmetric products hyperspace compact subsets prove has shadowing h shadowing only has shadowing h shadowing

Leobardo Fernández  1   ; Chris Good  1

1 School of Mathematics University of Birmingham Birmingham, United Kingdom B15 2TT 
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Leobardo Fernández; Chris Good. Shadowing for induced maps of hyperspaces. Fundamenta Mathematicae, Tome 235 (2016) no. 3, pp. 277-286. doi: 10.4064/fm136-2-2016

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