Topological Transitivity of Nonautonomous Dynamical Systems

Abstract

This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including intersection of any pair of open sets and existence of a dense orbit) that could be taken as definitions of the topological transitivity of a nonautonomous system, and addresses their relation both in the case of a general compact metric space and in the case where, in addition, the space has no isolated point. This provides the necessary basis for further investigation of transitivity of nonautonomous dynamical systems.