Furstenberg families and chaos on uniform limit maps

Let ( f n ) be a given sequence of continuous selfmaps of a compact metric space X which converges uniformly to a continuous selfmap f of a compact metric space X , and let F , F 1 , and F 2 be given Furstenberg families. In this paper, we obtain an equivalence condition for the uniform limit map f to be F -transitive or weakly F -sensitive or F -sensitive or ( F 1 , F 2 ) -sensitive and a necessary condition for the uniform limit map f to be weakly F -sensitive or F -sensitive or ( F 1 , F 2 ) -sensitive. Our results extend and improve some existing ones.