论文标题
惠特尼（Whitney）与随机驱动器的问题的Lyapunov指数
Lyapunov exponent for Whitney's problem with random drive
论文作者
论文摘要
我们考虑了由外力激发的倒置摆的惠特尼问题中不倾斜轨迹的统计特性。在外力是白噪声的情况下，我们最近使用超对称场理论的转移 - 矩阵分析在无限的时间间隔内在无限的时间间隔内发现了瞬时分布函数。在这里，我们将我们的方法推广到有限的时间间隔和多点相关函数的情况下。使用开发的形式主义，我们计算了Lyapunov指数，该指数确定了非垂直轨迹上相关的衰减率。
We consider the statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case when the external force is white noise, we recently found the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval using a transfer-matrix analysis of the supersymmetric field theory. Here, we generalize our approach to the case of finite time intervals and multipoint correlation functions. Using the developed formalism, we calculate the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory.
