We consider the billiard dynamics in a non-compact set of R^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
M. Seri, M. Lenci, M. Degli Esposti, G. Cristadoro (2011). Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two. JOURNAL OF STATISTICAL PHYSICS, 144, 124-138 [10.1007/s10955-011-0244-5].
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
LENCI, MARCO;DEGLI ESPOSTI, MIRKO;CRISTADORO, GIAMPAOLO
2011
Abstract
We consider the billiard dynamics in a non-compact set of R^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 propertiesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.