Topological Transitivity of Nonautonomous Dynamical Systems

TL;DR

This paper investigates the concept of topological transitivity in nonautonomous dynamical systems, analyzing various conditions and their relations to establish a foundational understanding for future research in this area.

Contribution

It provides a comprehensive analysis of different definitions of topological transitivity in nonautonomous systems and their interrelations on compact metric spaces.

Findings

Analyzes conditions for topological transitivity in nonautonomous systems

Establishes relations between different transitivity definitions

Provides foundational basis for future studies

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.