The transition between synchronization and chaos for random Blaschke products

2026/07/16 by Cecilia González-Tokman, Renee Oldfield
#math.DS

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Abstract

In this paper, we establish sufficient conditions for which a class of random circle maps, the so-called random Blaschke products, exhibits either synchronization or chaotic dynamics. We also establish necessary and sufficient conditions for such systems to have a unique random fixed point attractor in the unit disc. As an example, for a class of two map cocycles, we identify the random physical measures as a parameter is varied and investigate the critical value where the dynamics transitions from order to chaos.

Citations

• Synchronization rates and limit laws for random dynamical systems

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