论文标题
间隔图的相关总和和复发决定论
Correlation sum and recurrence determinism for interval maps
论文作者
论文摘要
复发定量分析是一种测量动力学系统复杂性的方法。复发确定性是IT的基本特征，与相关总和密切相关。在本文中，我们研究了这些量的间隔图的渐近行为。我们显示在哪些情况下存在渐近相关总和。一个零熵的间隔图和带有有限$ω$ - 限制设置的点的示例，并为其为其渐近相关总和不存在。此外，我们提出了分别相对于$ω$限制设置的基数或分别构成其间隔的配置的渐近相关总和计算的公式。我们还表明，对于不含有李约克的混乱（因此零熵）的间隔图，复发确定性的极限作为距离阈值收敛到零的限制可能严重小于一个。
Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior of these quantities for interval maps. We show for which cases the asymptotic correlation sum exists. An example of an interval map with zero entropy and a point with the finite $ω$-limit set for which the asymptotic correlation sum does not exist is given. Moreover, we present formulas for computation of the asymptotic correlation sum with respect to the cardinality of the $ω$-limit set or to the configuration of the intervals forming it, respectively. We also show that for a not Li-Yorke chaotic (and hence zero entropy) interval map, the limit of recurrence determinism as distance threshold converges to zero can be strictly smaller than one.
