On the Spectral Equivalence of Koopman Operators through Delay Embedding

Yoshihiko Susuki, Kyoichi Sako, Takashi Hikihara

Published 2017-06-03Version 1

We provide one theorem of spectral equivalence of Koopman operators of an original dynamical system and its reconstructed one through the delay-embedding technique. The theorem is proved for measure-preserving maps (e.g. dynamics on compact attractors) and provides a mathematical foundation of computing spectral properties of the Koopman operators by a combination of extended dynamic mode decomposition and delay-embedding.