Unique ergodicity for random noninvertible maps on an interval

In this short note, we investigate noninvertible stochastic dynamical systems on the unit interval <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> . We provide a handy condition for unique ergodicity for systems that are injective in mean. On the other hand, we give concrete examples where unique ergodicity fails.

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Publication Details

Journal
Annales de l’institut Fourier
Published
2026-03-26
DOI
https://doi.org/10.5802/aif.3770
Primary Topic
Mathematical Dynamics and Fractals
Type
article
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article

Unique ergodicity for random noninvertible maps on an interval

Hanna Oppelmayer, Sara Brofferio, Tomasz Szarek
Annales de l’institut Fourier
Mathematical Dynamics and Fractals
article

Unique ergodicity for random noninvertible maps on an interval

Hanna Oppelmayer, Sara Brofferio, Tomasz Szarek
article en

Abstract

In this short note, we investigate noninvertible stochastic dynamical systems on the unit interval <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> . We provide a handy condition for unique ergodicity for systems that are injective in mean. On the other hand, we give concrete examples where unique ergodicity fails.

Annales de l’institut Fourier
Centre National de la Recherche Scientifique (FR), Universität Innsbruck (AT), Université Paris-Est Créteil (FR), Instytut Oceanologii Polskiej Akademii Nauk (PL), Laboratoire d’Analyse et de Mathématiques Appliquées (FR), Université Gustave Eiffel (FR)
Openalex Percentile: Top 5%
Mathematical Dynamics and Fractals
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Unique ergodicity for random noninvertible maps on an interval — Hanna Oppelmayer, Sara Brofferio, et al. · Annales de l’institut Fourier (2026) | TGRS Research Map | TGRS