This repository outlines two computational approaches for approximating the continuous spectrum of the Koopman operator of dynamical systems
Method 1: using classical spectral estimation of stochastic signals from
"Study of dynamics in post-transient flows using Koopman mode decomposition"
Physical Review Fluids 2017, by H. Arbabi and I. Mezic (https://arxiv.org/pdf/1704.00813.pdf).
Method 2: apprximating the Koopman spectral measure using Fourier moments and Christoffel-Darboux kernel from
"Data-driven spectral analysis of the Koopman operator"
arXiv, by M. Korda, M. Putinar and I. Mezic (https://arxiv.org/pdf/1710.06532.pdf).
Spectrum_SP: Method 1 for Arnold's cat map, Lorenz 63, 2d cavity flow
Spectrum_CD: Method 2 for Arnold's cat map, Lorenz 63, 2d cavity flow and a synthetic example
send comments and questions to korda.m@gmail.com or arbabiha@gmail.com
Hassan Arbabi and Milan Korda
April 2018