Koopman算符在埃农映射中的动力学

In reality, most systems are usually difficult to describe with accurate equations of motion due to their complexity. Only some system data can be observed. We hope to extract the key features of the dynamical system through the observed data of the system. The dphase space of the system is partitioned to different patches accordingly. The Koopman operator provides an effective mathematical tool, which describes the evolution of the observable in the phase space and can be used to extract the characteristic modes of a nonlinear system. We partition the phase space of the H\'{e}non map by calculating the eigenvalues and eigenfunctions of the Koopman operator, and study the relationship between the stable manifold and the unstable manifold of the H\'{e}non map, the periodic orbit and the eigenfunction of the Koopman operator , Which provides a possible method for analyzing complex dynamics in high-dimensional nonlinear systems