On stochasticity in nearly-elastic systems
Probability
2012-08-31 v1 Dynamical Systems
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.
Cite
@article{arxiv.1203.5468,
title = {On stochasticity in nearly-elastic systems},
author = {Mark Freidlin and Wenqing Hu},
journal= {arXiv preprint arXiv:1203.5468},
year = {2012}
}
Comments
35 pages, 12 figures, already online at Stochastics and Dynamics