A note on ℱ-sensitivity for non-autonomous systems

Abstract

ABSTRACTWe study some stronger forms of sensitivity, namely, -sensitivity and weakly -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 -sensitivity and some other stronger forms of sensitivity through examples. We explore the relation between the -sensitivity of the non-autonomous system and autonomous system , where is a sequence of continuous functions converging uniformly to f. We also study the -sensitivity of a non-autonomous system , generated by a finite family of maps and give an example showing that such non-autonomous systems can be -sensitive, even when none of the maps in the family is -sensitive.