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On the Spectral Equivalence of Koopman Operators through Delay Embedding (1706.01006v1)
Published 3 Jun 2017 in math.DS and nlin.CD
Abstract: 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.
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