Dynamic mode decomposition for analytic maps
Provides theoretical justification for EDMD modes in complex dynamical systems, but is incremental as it extends known operator theory to a specific function space.
The paper shows that extended dynamic mode decomposition (EDMD) identifies modes corresponding to compact Perron-Frobenius and Koopman operators on Hardy-Hilbert spaces for analytic maps, elucidating the interpretation of EDMD spectra.
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.