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 one can prove that, under
general conditions, almost every system in the ensemble is recurrent.
The result can be extended to more exotic two-dimensional tubes and to
a fairly large class of d-dimensional tubes, with d > 2.
(Joint work with G. Cristadoro and M. Seri)