Infinite ergodic index of the ehrenfest wind-tree model

Minimality of the Ehrenfest wind-tree model

We consider aperiodic wind-tree models, and show that for a generic (in the sense of Baire) configuration the wind-tree dynamics is minimal in almost all directions, and has a dense set of periodic points.

Ehrenfest风树模式的典型递推式

Typical recurrence for the ehrenfest wind-tree model

我们表明，典型的风树模型，在Baire的意义下，是经常性的，并有一个密集的周期轨道集。递归的结果也适用于洛伦兹气体：典型的洛伦兹气体，在贝尔意义下，是递归的。这些洛仑兹气体不一定是有限视界的！

Ehrenfest Wind-Tree Model is Dynamically Richer Than the Lorentz Gas

We consider a physical Ehrenfests' Wind-Tree model where a moving particle is a hard ball rather than (mathematical) point particle. We demonstrate that a physical periodic Wind-Tree model is dynamically richer than a physical or mathematical periodic Lorentz gas. Namely, the physical Wind-Tree model may have diffusive behavior as the Lorentz gas does, but it has more superdiffusive regimes than the Lorentz gas. The new superdiffusive regime where the diffusion coefficient D(t)~(ln t)^2 of dynamics seems to be never observed before in any model.

Unique Ergodicity For Infinite Area Translation Surfaces

We consider infinite staircase translation surfaces with varying step sizes. For typical step sizes we show that the translation flow is uniquely ergodic in almost every direction. Our result also hold for typical configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology. In contrast, we show that the translation flow on a periodic translation surface can not be uniquely ergodic in any direction.

Escherichfest风树模型：周期方向，递归，扩散

The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion

我们研究周期性风树模型，无界平面台球周期性地位于矩形障碍物。对于一类合理的参数，我们证明了存在的完全周期性的方向，和复发;对于另一类合理的参数，有方向，所有的轨迹逃脱，我们证明了几乎所有方向的逃逸率。这些结果扩展到密集的参数$G_δ$。

埃伦费斯特风树台球的平均扩散速率

Average diffusion rate of Ehrenfest Wind-tree billiards

本文针对埃伦费斯特风树台球及更一般的闭平移曲面$\u2124^d$覆叠上的平坦测地射线，证明其平均扩散速率与最大扩散速率一致，均由相关李雅普诺夫指数决定，填补了此前仅知最大扩散速率的研究空白。