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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.

MSC:
 37B99 Topological dynamics
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References:
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