Random iterations of homeomorphisms on the circle

TL;DR

This paper investigates the behavior of random iterations of homeomorphisms on the circle, revealing how such systems can be understood through non-expansive average iterated function systems.

Contribution

It introduces a novel analysis framework for minimal homeomorphism systems on the circle using non-expansive average properties.

Findings

Systems can be characterized by non-expansive behavior on average.

Random iterations exhibit specific convergence properties.

The approach applies to minimal homeomorphism systems on the circle.

Abstract

We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function systems with probabilities which are non-expansive on average.