Asymptotically almost periodic points and sensitivity of continuous maps

Abstract

In this paper, the sensitivity of continuous self-maps is studied, containing transitive maps and non-transitive maps. The concepts of asymptotically almost periodic points and uniformly segment-recurrent points are raised, which are generalizations of the concept of almost periodic points. The concept of allured sets is also introduced, which is the opposite concept of ω-limit sets. By means these concepts, we obtain some conditions for a continuous map f from a metric space X to itself to be sensitive. Our results are generalizations of the main theorems given in [2,4,8,15,24,27].