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In this paper, we study geometric features of orientation-preserving randomdynamical systems on the circle driven by memoryless noise that exhibit stablesynchronisation: we consider crack points, invariant measures, and the linkbetween synchronisation and compressibility of arcs; we also characterisestable synchronisation in additive-noise stochastic differential equations onthe circle, in terms of "subperiodicity" of the vector field.

Synchronisation in Invertible Random Dynamical Systems on the Circle