二维或三维绝热活塞的周期振荡
The periodic oscillation of an adiabatic piston in two or three dimensions
摘要：
我们研究了一个质量为$M$的重活塞，它分离了许多理想的、在二维或三维空间中运动的单位质量气体粒子。Neishtadt和Sinai先前确定了一种方法来找到这个系统的平均方程，并表明它的解决方案周期性振荡。使用平均技术，我们证明了实际的活塞运动的概率收敛到预测的时间尺度$M^ {1/2} $上的平均行为时，$M$趋于无穷大，而系统的总能量是有界的，气体粒子的数量是固定的。
英文摘要：
We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted averaged behavior on the time scale $M^ {1/2} $ when $M$ tends to infinity while the total energy of the system is bounded and the number of gas particles is fixed.
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