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

TL;DR

This paper extends the understanding of Li-Yorke chaos in dynamical systems by using s-limit shadowing to create a global partition of the phase space, providing a comprehensive description of chaos types.

Contribution

It introduces a method to partition the phase space via chain components and applies s-limit shadowing to describe Li-Yorke chaos globally.

Findings

Partition of phase space into $G_\delta$-sets for chain components

Global description of Li-Yorke chaos for various Furstenberg families

Extension of chain proximal relation to continuous self-maps

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.