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Journal Articles Physica D: Nonlinear Phenomena Year : 2011

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

Abstract

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.
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Dates and versions

hal-00581551 , version 1 (31-03-2011)
hal-00581551 , version 2 (09-04-2011)
hal-00581551 , version 3 (18-07-2011)

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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⟩
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