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math.DS2026
Lift-Free Approaches to Random Rotation Number and Numerical Approximation
Zixu Li, Simon Lloyd
We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any cho…
math.DS2026
Periodicity and Rotation Number for Random Circle Homeomorphisms
Zixu Li, Simon Lloyd
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycl…