S-limit shadowing and a global description of Li-Yorke type chaos

Abstract

For any continuous self-map of a compact metric space, we extend a partition of each chain component with respect to a chain proximal relation to a $G_\delta$-partition of the phase space. Under the assumption of s-limit shadowing, we use this partition to give a global description of Li-Yorke type chaos corresponding to several Furstenberg families.