论文标题
匹配动态系统的观察结果，以及用于序列匹配的应用
Matching of observations of dynamical systems, with applications to sequence matching
论文作者
论文摘要
我们研究了沿着快速混合动力学系统的不同轨迹计算出的通用平滑观察结果之间最接近的相遇的统计分布。在大型轨迹的极限下，我们获得了牙龈类型的分布，该分布取决于轨迹的长度和图像度量的广义尺寸。它也受到一个极端指数的调节，该指数介绍了附近观察的趋势以及动力学的演变。我们为此数量提供了一类间隔和常规观察的混乱图。我们介绍了说明理论的多种数值应用，并讨论了这些结果对物理系统研究的含义。最后，我们讨论了此问题与不同符号序列共有的最长匹配块之间的联系。特别是，我们获得了强烈混合过程的分布结果。
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of Gumbel type that depends on both the length of the trajectories and on the Generalized Dimensions of the image measure. It is also modulated by an Extremal Index, that informs on the tendency of nearby observations to diverge along with the evolution of the dynamics. We give a formula for this quantity for a class of chaotic maps of the interval and regular observations. We present diverse numerical applications illustrating the theory and discuss the implications of these results for the study of physical systems. Finally, we discuss the connection between this problem and the problem of the longest matching block common to different sequences of symbols. In particular, we obtain a distributional result for strongly mixing processes.
