# Hartman-Grobman Theorem for IFS

## TL;DR

This paper extends the Hartman-Grobman theorem to one-dimensional iterated function systems on R and explores the concept of structural stability within this context.

## Contribution

It generalizes the classical Hartman-Grobman theorem to IFS and introduces the notion of structural stability for these systems.

## Key findings

- Generalized Hartman-Grobman theorem for IFS on R
- Defined structural stability for IFS
- Identified necessary conditions for stability

## 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.