Uniform structure with Iterated function System, Step Skew Product and Their Uniform Entropy

Abstract

In this paper, we will discuss some properties of finite uniform structures and introduce a uniform structure on step skew product of an iterated function system(IFS), then prove the equivalence of almost all topological properties between iterated function system(IFS) and corresponding step skew product. we generalize two very famous definitions of uniform entropy to IFS and after prove the basic properties, prove relation of uniform entropy of this systems and uniform entropy of corresponding step skew product.