Spontaneously stochastic Arnold's cat

We propose a simple model for the phenomenon of Eulerian spontaneous stochasticity in turbulence. This model is solved rigorously, proving that infinitesimal small-scale noise in otherwise a deterministic multi-scale system yields a large-scale stochastic process with Markovian properties. Besides its theoretical value, our model opens new ways for the experimental verification of spontaneous stochasticity in optics and electronics, and suggests new applications beyond fluid dynamics.

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