Transitivity in CR-Dynamical Systems

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.