Escherichfest风树模型：周期方向，递归，扩散
The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion
摘要：
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$G_δ$。
英文摘要：
We study periodic wind-tree models, unbounded planar billiards with periodically located rectangular obstacles. For a class of rational parameters we show the existence of completely periodic directions, and recurrence; for another class of rational parameters, there are directions in which all trajectories escape, and we prove a rate of escape for almost all directions. These results extend to a dense $G_δ$ of parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
