Unique ergodicity for random noninvertible maps on an interval

2024/01/22 by Sara Brofferio, Hanna Oppelmayer, Brofferio, Sara +3
Mathematics · #28D20 (Secondary) #37A50 #37E05 (Primary) 60G10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2401.12361

openalex publication_date 2024/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we investigate non-invertible stochastic dynamical systems on the unit interval [0, 1]. 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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