Topological transitivity in quasi-continuous dynamical systems

Abstract

A quasi-continuous dynamical system is a pair (X,f) consisting of a topological space X and a mapping f:X→X such that fn is quasi-continuous for all n∈N, where N is the set of non-negative integers. In this paper, we show that under appropriate assumptions, various definitions of the concept of topological transitivity are equivalent in a quasi-continuous dynamical system. Our main results establish the equivalence of topological and point transitivity in a quasi-continuous dynamical system. These extend some classical results on continuous dynamical systems in [3], [10] and [24], and some results on quasi-continuous dynamical systems in [7] and [8].