Weak near periodicity in dynamical systems

Abstract

Ahman and Elaydi introduced the concept of near periodicity and said that the notion of near periodicity of a dynamical system is somewhere between periodicity and almost periodicity. In particular, they claimed that a periodic dynamical system with no rest point is necessarily nearly periodic and posed a question whether a periodic dynamical system with rest points is nearly periodic or not. In this paper, we give an answer to the question and introduce the notion of weak near periodicity which is weaker than that of near periodicity. Some relationships between weak near periodicity and other dynamical properties are also studied