Infinite-horizon Lorentz tubes and gases: Recurrence and ergodic properties

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Lenci, Marco¹  Troubetzkoy, Serge^2,3 

[1] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

[2] CNRS, Ctr Phys Theor, F-13288 Marseille 9, France

[3] Federat Rech Unites Math Marseille, Marseille, France

关键词: Aperiodic;    Lorentz gas;    Quenched random dynamical systems;    Hyperbolic billiards;    Infinite ergodic theory;    Recurrence;   

DOI  :  10.1016/j.physd.2011.06.020

来源: Elsevier

【 摘 要 】

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincare) recurrent, uniformly hyperbolic, and ergodic, and the first-return map to any scatterer is K-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (ensembles) for which the above properties occur with probability 1. In the case of the Lorentz gases in the plane, we define families, endowed with a natural metric, within which the set of all chaotic dynamical systems is uncountable and dense. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free