TY - JOUR
T1 - Recurrence and Higher Ergodic Properties for Quenched Random Lorentz Tubes in Dimension Bigger than Two
AU - Seri, Marcello
AU - Lenci, Marco
AU - degli Esposti, Mirko
AU - Cristadoro, Giampaolo
PY - 2011/7
Y1 - 2011/7
N2 - We consider the billiard dynamics in a non-compact set of a"e (d) that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing 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.
AB - We consider the billiard dynamics in a non-compact set of a"e (d) that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing 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.
KW - Hyperbolic billiards
KW - Lorentz gas
KW - Infinite-measure dynamical systems
KW - Infinite ergodic theory
KW - Random environment
KW - Channel
KW - Tube
KW - SEMI-DISPERSING BILLIARDS
KW - FUNDAMENTAL THEOREM
KW - METALLIC BODIES
KW - HYPERBOLICITY
KW - MOTION
KW - GAS
U2 - 10.1007/s10955-011-0244-5
DO - 10.1007/s10955-011-0244-5
M3 - Article
SN - 0022-4715
VL - 144
SP - 124
EP - 138
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1
ER -