等变动力系统全局相空间探索的Koopman算子方法
Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems
摘要：
本文发展了具有对称性的动力系统的Koopman算子理论。特别是，我们调查如何Koopman运营商和本征函数的基础动力系统的对称群的作用下的行为。此外，探索潜在的对称性，我们提出了一个算法来构建一个全球Koopman运营商从本地Koopman运营商。特别是，我们表明，通过利用对称性，从所有的不变集的数据是不需要构建的全球Koopman算子，也就是说，当地的知识系统是足以推断的全球动态。
英文摘要：
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.
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