Exploring F-Sensitivity for Non-Autonomous Systems

TL;DR

This paper investigates stronger forms of sensitivity in non-autonomous discrete dynamical systems, establishing conditions for their equivalence, and exploring their relationships with autonomous systems and systems generated by finite map families.

Contribution

It introduces and analyzes F-sensitivity and weakly F-sensitivity, providing conditions for their equivalence and examining their behavior in various non-autonomous contexts.

Findings

F-sensitivity and weakly F-sensitivity are equivalent under certain conditions.

Non-autonomous systems can be F-sensitive even if individual maps are not.

The relation between F-sensitivity in non-autonomous and autonomous systems is characterized.

Abstract

We study some stronger forms of sensitivity, namely, F-sensitivity and weakly F-sensitivity for non-autonomous discrete dynamical systems. We obtain a condition under which these two forms of sensitivity are equivalent. We also justify the difference between F-sensitivity and some other stronger forms of sensitivity through examples. We explore the relation between the F-sensitivity of the non-autonomous system (X, f1;infinity) and autonomous system (X, f), where fn is a sequence of continuous functions converging uniformly to f. We also study the F-sensitivity of a non-autonomous system (X, f1;infinity), generated by a finite family of maps F = f1, f2, : : : , fk and give an example showing that such non-autonomous systems can be F-sensitive, even when none of the maps in the family F is F-sensitive.