A dynamical version of Kuratowski-Mycielski Theorem and invariant chaotic sets

TL;DR

This paper develops a dynamical extension of the Kuratowski-Mycielski Theorem to identify large invariant dependent sets, and applies it to analyze invariant chaotic sets, simplifying existing results and deriving new insights.

Contribution

It introduces a dynamical version of the Kuratowski-Mycielski Theorem and applies it to study invariant chaotic sets in topological dynamics, providing new theoretical tools.

Findings

Established a dynamical Kuratowski-Mycielski Theorem

Simplified existing results on invariant chaotic sets

Derived new results on the structure of invariant dependent sets

Abstract

We establish a dynamical version of Kuratowski-Mycielski Theorem on the existence of "large" invariant dependent sets. We apply this result to the study of invariant chaotic sets in topological dynamical systems, simplify many known results on this topic and also obtain some new results.