Analysis of Chaotic Phenomena by the Hitting Time Distribution of Dynamical Systems

通过对碰撞时间的分析，研究了混沌动力系统中非常复杂的运动的随机性质，即轨道撞击某一固定区域的时间。特别是在非一致双曲动力系统为“弱混沌”的情况下，我们发现了与典型混沌系统不同的分布。此外，我们还研究了相遇时间分布的随机性质，即不同轨道接近的时间。

We have studied the stochastic properties of chaotic dynamical systems in which very complex motions appear by the analysis of the hitting time, that is, the time in which an orbit hit to some fixed domain. Especially, in the case of non-uniformly hyperbolic dynamical system which is a "weak chaos", we showed that the different distribution from the one of the typical chaotic system appears. And, we also studied the stochastic properties of the meeting time distribution, that is, the time in which different orbits come close.