Linearization in the large of nonlinear systems and Koopman operator spectrum

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Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics (2013, background): “For higherdimensional systems (or two-dimensional systems with a sink node), global linearization involves several Koopman eigenfunctions sj(x) (see [20] for a detailed study), which can be obtained through the generalized Laplace averages (see Remark 3).”
Chaos as an intermittently forced linear system (2016, methodology): “For a detailed discussion on the Koopman operator, there are many excellent research articles [70, 82, 16, 17, 61] and reviews [18, 71].”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, methodology): “The dynamic mode decomposition (DMD) [237, 228, 269] is a promising new technique for system identification that has strong connections to nonlinear dynamical systems through Koopman spectral analysis [162, 163, 187, 47, 188, 170, 41].”