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Markovian random iterations of homeomorphisms of the circle

Part of: Low-dimensional dynamical systems Measure-theoretic ergodic theory Ergodic theory

Published online by Cambridge University Press:  21 July 2021

EDGAR MATIAS Open the ORCID record for EDGAR MATIAS [Opens in a new window]
EDGAR MATIAS*
Affiliation:
Departamento de Matemática, Universidade Federal da Bahia, Av. Adhemar de Barros s/n, Salvador40170-110, Brazil
*
e-mail: edgar.matias@ufba.br
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Abstract

In this paper we prove a local exponential synchronization for Markovian random iterations of homeomorphisms of the circle $S^{1}$ , providing a new result on stochastic circle dynamics even for $C^1$ -diffeomorphisms. This result is obtained by combining an invariance principle for stationary random iterations of homeomorphisms of the circle with a Krylov–Bogolyubov-type result for homogeneous Markov chains.

Keywords

random iteration of mapssynchronizationstationary measureskew productinvariant measure

MSC classification

Primary: 37E10: Maps of the circle
Secondary: 37A50: Relations with probability theory and stochastic processes 28D05: Measure-preserving transformations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 9 , September 2022 , pp. 2935 - 2956
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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