Li-Yorke Sensitivity of Set-Valued Discrete Systems - Heng Liu; Fengchun Lei; Lidong Wang (Journal of Applied Mathematics)
Consider the surjective, continuous map f:X→X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 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 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 f¯.