TYPICAL RECURRENCE FOR THE EHRENFEST WIND-TREE MODEL

Serge Troubetzkoy (1, 2, 3, 4)

1 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
2 CPT - Centre de Physique Théorique - UMR 6207
3 IML - Institut de mathématiques de Luminy
4 CPT - Centre de Physique Théorique - UMR 7332

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!

Domaines: Systèmes dynamiques [math.DS]

Serge Troubetzkoy. TYPICAL RECURRENCE FOR THE EHRENFEST WIND-TREE MODEL. Journal of Statistical Physics, 2010, pp.60-67. ⟨10.1007/s10955-010-0026-5⟩. ⟨hal-00474453⟩