Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two. (English) Zbl 1226.82056
Summary: We consider the billiard dynamics in a non-compact set of \(\mathbb R^d\) 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.
MSC:
| 37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
| 37A60 | Dynamical aspects of statistical mechanics |
Keywords:
hyperbolic billiards; Lorentz gas; infinite-measure dynamical systems; infinite ergodic theory; random environment; channel; tubeReferences:
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