Shadowing for induced maps of hyperspaces
Volume 235 / 2016
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].
