On stochasticity in nearly-elastic systems

Mark Freidlin, Wenqing Hu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number1150020
JournalStochastics and Dynamics
Issue number3
StatePublished - Sep 2012
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by NSF grants DMS-0803287 and DMS-0854982. We would like to thank the anonymous referee for carefully reading the manuscript.


  • Averaging principle
  • Hamiltonian flows
  • Markov processes on graphs
  • chaotic systems


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