Dynamic mode decomposition for analytic maps

Abstract

Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron-Frobenius and Koopman operators defined on suitable Hardy-Hilbert spaces when the method is applied to classes of analytic maps. Our findings elucidate the interpretation of the spectra obtained by EDMD for complex dynamical systems. We illustrate our results by numerical simulations for analytic maps.

arXiv comment14 pages. 3 figures

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Cited by in corpus (4)

• Fourier approximation of the statistical properties of Anosov maps on tori
• Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
• Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response
• Koopman and transfer operator techniques from the perspective of quantum theory