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

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are ‘chaotic’, in the sense that they are (Poincaré) 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.