arXiv:1905.09266 Abstract | arXiv Analytics

arXiv:1905.09266 [math.DS]Abstract References Reviews Resources

Dynamic mode decomposition for analytic maps

Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just

Published 2019-05-22Version 1

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.

Comments: 14 pages. 3 figures

Categories: math.DS, math.NA, nlin.CD

Subjects: 37M25, 37M10, 37E10, 37C30

Keywords: analytic maps, complex dynamical systems, extended dynamic mode decomposition, suitable hardy-hilbert spaces, koopman operators

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