INFINITE ERGODIC INDEX OF THE EHRENFEST WIND-TREE MODEL

Alba Málaga (1) , Serge Troubetzkoy (2)

1 CHART-THIM - Technologies, Handicaps, Interfaces et Multimodalités
2 I2M - Institut de Mathématiques de Marseille

The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree dynamics has infinite ergodic index in almost every direction. In particular some ergodic theorems can be applied to show that if we start with a large number of initially parallel particles their directions decorrelate as the dynamics evolve answering the question posed by the Ehrenfests.

Domaines: Systèmes dynamiques [math.DS]

Alba Málaga, Serge Troubetzkoy. INFINITE ERGODIC INDEX OF THE EHRENFEST WIND-TREE MODEL. 2017. ⟨hal-01433019v1⟩