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Markovian random iterations of homeomorphisms of the circle
Published online by Cambridge University Press: 21 July 2021
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.
MSC classification
Primary:
37E10: Maps of the circle
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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