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Creators/Authors contains: "Mailybaev, Alexei A"

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  1. ; ; (, Ergodic Theory and Dynamical Systems)
    Abstract We study a class of ordinary differential equations with a non-Lipschitz point singularity that admits non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on a parameter$$\nu $$: the regularized dynamics is globally defined for each$$\nu> 0$$, and the original singular system is recovered in the limit of vanishing$$\nu $$. We prove that this limit yields aunique statistical solutionindependent of regularization when the deterministic system possesses a chaotic attractor having a physical measure with the convergence to equilibrium property. In this case, solutions become spontaneously stochastic after passing through the singularity: they are selected randomly with an intrinsic probability distribution. 
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  2. ; (, Nonlinearity)
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