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Shadowing for induced maps of hyperspaces

Volume 235 / 2016

Leobardo Fernández, Chris Good Fundamenta Mathematicae 235 (2016), 277-286 MSC: Primary 37B99, 37C50, 54B20, 54H20. DOI: 10.4064/fm136-2-2016 Published online: 4 July 2016

Abstract

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].

Authors

  • Leobardo FernándezSchool of Mathematics
    University of Birmingham
    Birmingham, United Kingdom B15 2TT
    e-mail
    e-mail
  • Chris GoodSchool of Mathematics
    University of Birmingham
    Birmingham, United Kingdom B15 2TT
    e-mail

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