AI 中文总结
本文研究齐性空间上微分正系统的伯克霍夫中心结构与循环行为，建立其序结构二分性，完成循环动力学的完整刻画。
AI 中文摘要
我们研究了微分正系统的伯克霍夫中心的结构及其循环行为，这类系统的轨道线性化在齐性空间上保持齐性锥场。这类锥场自然产生于广义相对论与李理论。我们对伯克霍夫中心建立了序结构二分性：伯克霍夫中心的每个连通分支，以及任一不变测度的支撑集，要么是强序的，要么是无序的。这通过基础序关系的视角，给出了齐性空间上微分正系统循环动力学的完整刻画。
英文摘要
We study the structure of the Birkhoff center and the recurrent behavior of differentially positive systems whose linearizations along trajectories preserve a homogeneous cone field on a homogeneous space. Such cone fields arise naturally from general relativity and Lie theory. We establish an order-structural dichotomy for the Birkhoff center: every connected component of the Birkhoff center, as well as the support of any invariant measure, is either strongly ordered or unordered. This yields a comprehensive characterization of recurrent dynamics for differentially positive systems on homogeneous spaces, interpreted through the lens of the underlying order relation.
