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Sensitivity of set-valued discrete systems. (English) Zbl 1194.37034
Let $X$ be a compact metric space and $K(X)$ be the set of all nonempty compact subsets of $X$ equipped with the Hausdorff metric. In this paper, examples are given that sensivity of a surjective continuous map $f:X\to X$ does not imply sensivity of the induced continuous self-mapping $\bar f:K(X)\to K(X)$. Moreover, it is shown that if $f$ is a surjective continuous interval map, then $\bar f$ is sensitive if and only if $f$ has this property.

37B99Topological dynamics
Full Text: DOI
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