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Communications in Nonlinear Science and Numerical Simulation
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Dynamic mode decomposition for analytic maps

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2020Embargo end date: 01 Jan 2019 United Kingdom English Publisher:Elsevier BVJournal:Communications in Nonlinear Science and Numerical Simulation, volume 84, page 105,179 (issn: 1007-5704, Copyright policy )Funded by:UKRI | Transfer operator methods...
Authors: Slipantschuk, J; Bandtlow, OF; Just, W;

doi: 10.1016/j.cnsns.2020.105179 , 10.48550/arxiv.1905.09266

arXiv: http://arxiv.org/abs/1905.09266

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.

14 pages. 3 figures

Country
United Kingdom
Related Organizations
Keywords

FOS: Mathematics, FOS: Physical sciences, 37M25, 37M10, 37E10, 37C30, Mathematics - Numerical Analysis, Dynamical Systems (math.DS), Numerical Analysis (math.NA), Mathematics - Dynamical Systems, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics

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    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Top 10%
Average
Average
Green
hybrid