Random Dynamical Systems on the circle without a finite orbit

2025/01/21 by Dominique Malicet, Graccyela Salcedo, Malicet, Dominique +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2501.12158

Abstract

In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are finite unions of intervals. We describe the accumulation points of the average orbit of the transfer operator. For each ergodic stationary measure, we demonstrate interesting properties of its weight function on the circle. Relationships between the minimal sets of an RDS and its inverse RDS are also established.

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• Concentration inequalities for random dynamical systems

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