Conceptions of Topological Transitivity

TL;DR

This paper clarifies the relationships among various definitions of topological transitivity in dynamical systems, providing a comprehensive overview of their equivalences under different conditions.

Contribution

It offers a complete and accessible description of how different notions of topological transitivity relate, consolidating scattered results into a unified framework.

Findings

Different definitions of topological transitivity are equivalent under reasonable conditions.

The paper consolidates various partial results into a comprehensive overview.

Provides a clear reference for researchers in topological dynamics.

Abstract

There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various equivalences are proved in different places, but the full story is difficult to find. This note provides a complete description of the relationships among the different properties.