In this paper we propose an extension of Koopman operator framework for non-autonomous systems with periodic and quasi-periodic time dependence. Using a time parametrized family of Koopman operators and the associated time dependent eigenvalues and eigenfunctions, and concepts from Floquet theory, we extend the notion of the Koopman Mode Decomposition. We illustrate our framework on several examples.
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Mezić et al. (2016) studied this question.
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