论文标题
动力系统的投影嵌入：均匀的平均场方程
Projective Embedding of Dynamical Systems: uniform mean field equations
论文作者
论文摘要
我们通过投影仪操作员研究在较大维度中连续动力系统的嵌入。我们称这种技术为动态系统的投影嵌入，因为动态的稳定固定点是通过从较高维空间的投影中恢复的。在本文中，我们提供了一个一般定义，并证明，对于秩-1的特定类型的投影仪操作员，均匀的平均场投影仪，运动方程成为动力系统的平均场近似。虽然通常，嵌入取决于指定的变量排序，但对于均匀的平均场投影仪而言，嵌入方式并非如此。此外，我们证明原始稳定的固定点仍然是动力学的稳定固定点，鞍点仍然是鞍座，但不稳定的固定点成为鞍座。
We study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of projector operator of rank-1, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. In addition, we prove that the original stable fixed points remain stable fixed points of the dynamics, saddle points remain saddle, but unstable fixed points become saddles.
