Abstract
We show that the typical wind-tree model, in the sense of Baire, is recurrent and has a dense set of periodic orbits. The recurrence result also holds for the Lorentz gas: the typical Lorentz gas, in the sense of Baire, is recurrent. These Lorentz gases need not be of finite horizon!
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Troubetzkoy, S. Typical Recurrence for the Ehrenfest Wind-Tree Model. J Stat Phys 141, 60–67 (2010). https://doi.org/10.1007/s10955-010-0026-5
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DOI: https://doi.org/10.1007/s10955-010-0026-5