${\mathcal F}$-Hypercyclic and disjoint ${\mathcal F}$-hypercyclic properties of binary relations over topological spaces

TL;DR

This paper investigates ${ m extbf{F}}$-hypercyclic and disjoint ${ m extbf{F}}$-hypercyclic properties of binary relations over topological spaces, with a focus on finite structures like graphs and tournaments, including numerous examples.

Contribution

It introduces and analyzes ${ m extbf{F}}$-hypercyclic and disjoint ${ m extbf{F}}$-hypercyclic properties for binary relations, especially in finite topological structures, with extensive illustrative examples.

Findings

Characterization of ${ m extbf{F}}$-hypercyclic properties in finite structures

Examples demonstrating various ${ m extbf{F}}$-hypercyclic behaviors

Insights into disjoint ${ m extbf{F}}$-hypercyclicity in graphs and tournaments

Abstract

In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.