Shadowing in CR-Dynamical Systems

Abstract

A CR-dynamical system is a pair $(X, G)$, where $X$ is a non-empty compact Hausdorff space with uniformity $\mathscr{U}$ and $G$ is a closed relation on $X$. In this paper we introduce the $(i, j)$-shadowing properties in CR-dynamical systems, which generalises the shadowing property from topological dynamical systems $(X, f)$. This extends previous work on shadowing in set-valued dynamical systems.