关于刻画周期轨道压缩度量的矩阵值PDE
On a matrix-valued PDE characterizing a contraction metric for a periodic orbit
摘要：
周期轨道的稳定性和吸引区域可以使用收缩度量来确定，即，一种黎曼度量，相邻解相对于它收缩。收缩度量不需要知道周期轨道的位置，并且对扰动具有鲁棒性。本文刻画了一类线性一阶偏微分方程的矩阵值解的黎曼压缩度量。这将使明确的建设的收缩度规，数值求解此方程在未来的工作。本文证明了偏微分方程解的存在唯一性，并证明了它定义了一个压缩度量。
英文摘要：
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the position of the periodic orbit and is robust to perturbations. In this paper we characterize such a Riemannian contraction metric as matrix-valued solution of a linear first-order Partial Differential Equation. This will enable the explicit construction of a contraction metric by numerically solving this equation in future work. In this paper we prove existence and uniqueness of the solution of the PDE and show that it defines a contraction metric.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
