In this paper, we study geometric features of orientation-preserving random dynamical systems on the circle driven by memoryless noise that exhibit stable synchronisation: we consider crack points, invariant measures, and the link between synchronisation and compressibility of arcs; we also characterise stable synchronisation in additive-noise stochastic differential equations on the circle, in terms of "subperiodicity" of the vector field.
@article{arxiv.1502.07618,
title = {Synchronisation in Invertible Random Dynamical Systems on the Circle},
author = {Julian Newman},
journal= {arXiv preprint arXiv:1502.07618},
year = {2017}
}