Li-Yorke Sensitivity of Set-Valued Discrete Systems

Abstract EN

Consider the surjective, continuous map f:X→X and the continuous map f¯ of ?(X) induced by f, where X is a compact metric space and ?(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¯.