Li-Yorke sensitivity of set-valued discrete systems
Summary: Consider the surjective, continuous map \(f:X\to X\) and the continuous map \(\overline f\) of \(\mathcal K(X)\) induced by \(f\), where \(X\) is a compact metric space and \(\mathcal K(X)\) is the space of all nonempty compact subsets of \(X\) endowed with the Hausdorff metric. In this paper, we give a short proof that if \(\overline f\) is Li-Yoke sensitive, then \(f\) is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of \(f\) does not imply Li-Yorke sensitivity of \(\overline f\).
scientific article; zbMATH DE number 6950588