Transitivity in CR-Dynamical Systems

TL;DR

This paper introduces new concepts of transitivity and transitive points in CR-dynamical systems, along with a novel tool called transitivity trees to analyze their relationships.

Contribution

It presents a new framework for understanding transitivity in CR-dynamical systems and develops transitivity trees as a novel analytical tool.

Findings

Defined new types of transitive points in CR-dynamical systems

Established relationships between different transitivity types using transitivity trees

Provided a systematic method to analyze transitivity properties

Abstract

A CR-dynamical system is a pair $(X, G)$, where $X$ is a compact metric space and $G$ is a closed relation (CR) on $X$. In this paper, we introduce a new type of transitive point and transitivity in CR-dynamical systems. We develop a new tool called transitivity trees, which we use to determine the relationship between the different types of transitive points.