- 09-170 Giampaolo Cristadoro, Marco Lenci, Marcello Seri
- Recurrence for quenched random Lorentz tubes
Sep 16, 09
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Abstract. We consider the billiard dynamics in a cylinder-like set that is tessellated by countably many translated copies of the same d-dimensional polytope. 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'. For d=2 we prove that, under general conditions, almost every system in the ensemble is recurrent. We then extend the result to more exotic two-dimensional tubes and to a fairly large class of d-dimensional tubes, with d > 2.