论文标题
Koopman操作员方法用于全球阶段空间探索模棱两可的动力学系统
Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems
论文作者
论文摘要
在本文中，我们开发了具有对称性动力学系统的Koopman操作员理论。特别是，我们研究了Koopman操作员和本征函数如何在基础动力学系统的对称组的作用下行为。此外，在探索基础对称性的情况下，我们提出了一种算法来构建本地Koopman运营商的全球Koopman操作员。特别是，我们通过利用对称性来证明，构造全局koopman运算符的所有不变集的数据并不需要。也就是说，对系统的本地知识足以推断全球动态。
In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical system. Further, exploring the underlying symmetry, we propose an algorithm to construct a global Koopman operator from local Koopman operators. In particular, we show, by exploiting the symmetry, data from all the invariant sets are not required for constructing the global Koopman operator; that is, local knowledge of the system is enough to infer the global dynamics.
