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

Details Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties

2011-03-31

arxiv.org/abs/1103.6110v3

Mathematics

Dynamical Systems

Final version, to appear in Physica D (2011)

Scientific paper

10.1016/j.physd.2011.06.020

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincar\'e) recurrent, uniformly hyperbolic, 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 (\emph{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.

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