Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 84, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2020.105179
Keywords
Dynamical mode decomposition; Koopman operator; Spectral convergence; Transfer operator
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Funding
- EPSRC [EP/R012008/1] Funding Source: UKRI
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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. Crown Copyright (C) 2020 Published by Elsevier B.V.
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