A Closed Graph Theorem for hyperbolic iterated function systems

TL;DR

This paper introduces a new concept of morphisms between hyperbolic iterated function systems, proving a Closed Graph Theorem that links morphism graphs to attractors, aiding in topological conjugacy analysis.

Contribution

It defines morphisms for hyperbolic iterated function systems and establishes a Closed Graph Theorem connecting morphism graphs to attractors, advancing the understanding of their structure.

Findings

Graph of a morphism is an attractor of an IFS

Provides a method to analyze topological conjugacy

Establishes a theoretical foundation for morphism analysis

Abstract

In this note we introduce a notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of a morphism is the attractor of an iterated function system, giving a Closed Graph Theorem, and show how it can be used to approach the topological conjugacy problem for iterated function systems.