Recurrence for quenched random Lorentz tubes

Chaos. 2010 Jun;20(2):023115. doi: 10.1063/1.3405290.


We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.