Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow

2025/04/20 by Jiang, Nianci, Zhang, Weili
#35Q49 #37A25 #37H05 #76F25 #76W05 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.14564

Abstract

For the long-time dynamical challenges of some prototypical 3D flows including the ABC flow on \mathbbT³, we apply a random splitting method to establish two fundamental indicators of chaotic dynamics. First, under general assumptions, we establish that these random splittings exhibit Lagrangian chaos, characterized by a positive top Lyapunov exponent. Furthermore, we demonstrate the almost-sure quenched correlation decay of these random splittings, which is a stronger property than the almost-sure positivity of Lyapunov exponents alone. This framework is then applied to construct ideal dynamo in kinematic dynamo theory and to establish exponential mixing of passive scalars.

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