Unique ergodicity for noninvertible function systems on an interval

TL;DR

This paper investigates conditions under which certain noninvertible function systems on the interval exhibit unique ergodicity, using bounded variation as a key analytical tool, and provides multiple example classes.

Contribution

It introduces new sufficient conditions for unique ergodicity in noninvertible interval systems based on bounded variation, with illustrative examples.

Findings

Established sufficient conditions for unique ergodicity

Identified classes of systems satisfying these conditions

Demonstrated the applicability through examples

Abstract

We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.