Invariants of Uniform Conjugacy on Uniform Dynamical System

Abstract

  In this paper, we present some important dynamical concepts on uniform space such as the uniform minimal systems, uniform shadowing, and strong uniform shadowing. We explain some definitions and theorems such as definition uniform expansive, weak uniform expansive, uniform generator, and the proof of the theorems for them. We prove that if  be a homeomorphism on a compact uniform space  then  has uniform shadowing if and only if has uniform shadowing, so if  has strong uniform shadowing if and only if has strong uniform shadowing. We also show that  and  be two uniform homeomorphisms on compact uniform spaces  and , if  is a uniform conjugacy from  to , then . Besides some other results.