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random iteration of maps

Ergodic Theory and Dynamical Systems (1)

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Markovian random iterations of homeomorphisms of the circle
Part of
EDGAR MATIAS
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 9 / September 2022

Published online by Cambridge University Press:

21 July 2021, pp. 2935-2956

Print publication:

September 2022
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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.