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

Marco Lenci (1) , Serge Troubetzkoy (2, 3, 4)

1 Dipartimento di Matematica
2 IML - Institut de mathématiques de Luminy
3 CPT - Centre de Physique Théorique - UMR 6207
4 CPT - Centre de Physique Théorique - UMR 7332

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, 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.

Domaines: Systèmes dynamiques [math.DS]

Marco Lenci, Serge Troubetzkoy. Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties. Physica D: Nonlinear Phenomena, 2011, 10.1016/j.physd.2011.06.020. ⟨10.1016/j.physd.2011.06.020⟩. ⟨hal-00581551v3⟩