Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems

TL;DR

This paper investigates the relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems, revealing that these properties are not equivalent as in autonomous systems.

Contribution

It demonstrates that, unlike autonomous systems, positive topological sequence entropy and Li-Yorke chaos do not imply each other in nonautonomous systems.

Findings

Positivity of topological sequence entropy does not imply Li-Yorke chaos.

Li-Yorke chaos does not imply positive topological sequence entropy.

The relationship between these chaotic properties differs from autonomous systems.

Abstract

We study chaotic properties of uniformly convergent nonautonomous dynamical systems. We show that, contrary to the autonomous systems on the compact interval, positivity of topological sequence entropy and occurrence of Li-Yorke chaos are not equivalent, more precisely, neither of the two possible implications is true.