Recurrence and Higher Ergodic Properties for Quenched Random Lorentz Tubes in Dimension Bigger than Two
Abstract
We consider the billiard dynamics in a noncompact set of &R;^{ d } that is constructed as a biinfinite chain of translated copies of the same ddimensional polytope. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.
 Publication:

Journal of Statistical Physics
 Pub Date:
 July 2011
 DOI:
 10.1007/s1095501102445
 arXiv:
 arXiv:1011.6414
 Bibcode:
 2011JSP...144..124S
 Keywords:

 Hyperbolic billiards;
 Lorentz gas;
 Infinitemeasure dynamical systems;
 Infinite ergodic theory;
 Random environment;
 Channel;
 Tube;
 Mathematics  Dynamical Systems;
 37D50;
 37A40;
 60K37;
 37B20
 EPrint:
 Final version for J. Stat. Phys., 18 pages, 4 figures