Unified dynamical systems on coarse spaces

TL;DR

This paper introduces coarse dynamical systems on coarse spaces, explores their properties like conjugacy and coproducts, and extends the concept to set-valued systems, advancing the understanding of dynamics in coarse geometry.

Contribution

It defines coarse dynamical systems and coarse conjugacy, studies their properties, and extends the framework to set-valued systems, providing new insights in coarse geometry dynamics.

Findings

Coproduct of two coarse dynamical systems is a coarse dynamical system

Coarse conjugacy preserves set-valued coarse dynamical systems

Introduces set value coarse dynamical systems and their conjugacy

Abstract

In this paper, we introduce a new class of dynamical systems on a coarse space with coarse time called, coarse dynamical system. The notion of coarse conjugacy is studied from coarse geometry point of view. Coarse orbits as invariant sets under coarse conjugacy are deduced. It is Shown that the coproduct of two coarse dynamical systems is a coarse dynamical system. Finally, we define set value coarse dynamical systems and prove if two coarse dynamical systems are coarse conjugate, then their corresponding set value coarse dynamical systems are coarse conjugate