Adding Machine Maps and Minimal Sets for Iterated Function Systems

TL;DR

This paper extends the concept of adding machine maps to iterated function systems, establishing conditions for conjugacy and exploring minimal systems and tent maps in a topological context.

Contribution

It provides necessary and sufficient conditions for conjugacy of iterated function systems to adding machine maps and analyzes minimal systems with non-periodic points.

Findings

Minimal IFS with non-periodic points are semi-conjugate to adding machine maps.

Conditions for topological conjugacy of IFS to adding machine maps are established.

Investigation of conjugacy in infinite families of tent maps and their omega-limit sets.

Abstract

In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be conjugated to an adding machine map. It is proved that every minimal iterated function system which has some non-periodic regular point is semi-conjugate to an adding machine map. Furthermore, we investigate the topological conjugacy of an infinite family of tent maps, as well as the restriction of a map to its $\omega-$limit set with an iterated function system.