Some results on s-limit shadowing and Li-Yorke type chaos

TL;DR

This paper explores the relationship between s-limit shadowing and Li-Yorke chaos in compact metric spaces, extending previous results to more general Furstenberg families and providing illustrative examples.

Contribution

It generalizes earlier findings by analyzing s-limit shadowing with broader Furstenberg families and offers new insights into Li-Yorke chaos in this context.

Findings

Extended the description of Li-Yorke chaos to general Furstenberg families.

Provided an example illustrating the theoretical results.

Connected s-limit shadowing with chaos in compact metric spaces.

Abstract

In [13], for any continuous self-map of a compact metric space with s-limit shadowing, by using a $G_\delta$-partition of the phase space, a global description of Li-Yorke type chaos (with respect to several particular Furstenberg families) is obtained. In this paper, we complement the results in [13] by some results concerning the s-limit shadowing and general Furstenberg families. An example is also given to illustrate the results.