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Synchronization properties of random piecewise isometries. (English) Zbl 1361.37053

Summary: We study the synchronization properties of the random double rotations on tori. We give a criterion that show when synchronization is present in the case of random double rotations on the circle and prove that it is always absent in dimensions two and higher.

MSC:

37H10 Generation, random and stochastic difference and differential equations
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
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