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arXiv · 1203.5468

On stochasticity in nearly-elastic systems

Mark Freidlin·Wenqing Hu
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Abstract

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to stochasticity of its long-time behavior. Various ways to give a rigorous meaning to the last statement are considered. All of them, if applicable, lead to the same stochasticity which is described explicitly. So that the stochasticity of the long-time behavior is an intrinsic property of the deterministic systems.

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Mark Freidlin, Wenqing Hu. 2012-03-25. On stochasticity in nearly-elastic systems. https://doi.org/10.1142/s0219493711500201

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