Hartman-Grobman Theorem for IFS

Abstract

In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for one dimensional iterated function systems on R. Also, we introduce the basic concept of structural stability for an iterated function system and so we investigate the necessary condition for structural stability of an iterated function system on R.