Variations on the Concept of Topological Transitivity

TL;DR

This paper explores different strengthened versions of topological transitivity, especially in non-invertible systems, and maps out the logical relationships among ten related notions.

Contribution

It introduces and analyzes various strengthened concepts of topological transitivity and clarifies their implications in non-invertible dynamical systems.

Findings

Identifies ten notions of transitivity and their implications.

Highlights differences between invertible and non-invertible systems.

Provides a structured framework for understanding transitivity properties.

Abstract

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among ten reasonable notions of transitivity.