论文标题
Ruelle公式用于混乱系统中统计的线性响应的计算实现
A computable realization of Ruelle's formula for linear response of statistics in chaotic systems
论文作者
论文摘要
我们为混沌系统的Ruelle线性响应公式提供了可计算的重新进行的重新进行重新重新制定。使用$ n $相位点的新公式（称为Space-Split灵敏度或S3）实现了$ {\ cal O}（1/\ sqrt {n}）$的订单的错误收敛性。重新制定是基于将整体敏感性分解为扰动的稳定和不稳定组成部分的基础。对灵敏度的不稳定贡献是使用梯形特性和动力学的双曲线结构正规化的。均匀双曲线吸引子的数值示例用于验证S3公式，以针对幼稚的有限差异计算。敏感性密切匹配，S3所需的样本点要少得多。
We present a computable reformulation of Ruelle's linear response formula for chaotic systems. The new formula, called Space-Split Sensitivity or S3, achieves an error convergence of the order ${\cal O}(1/\sqrt{N})$ using $N$ phase points. The reformulation is based on splitting the overall sensitivity into that to stable and unstable components of the perturbation. The unstable contribution to the sensitivity is regularized using ergodic properties and the hyperbolic structure of the dynamics. Numerical examples of uniformly hyperbolic attractors are used to validate the S3 formula against a naïve finite-difference calculation; sensitivities match closely, with far fewer sample points required by S3.
