Recurrence for quenched random Lorentz tubes

Giampaolo Cristadoro, Marco Lenci, Marcello Seri

Published 2009-09-16, updated 2010-11-19Version 2

We consider the billiard dynamics in a strip-like 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.