Unified dynamical systems on coarse spaces

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