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We propose an algorithm that combines Proper Orthogonal Decomposition with a spectral method to analyse and extract from time data series of velocity fields, reduced order models of flows. The flows considered in this study are assumed to be driven by non linear dynamical systems exhibiting a complex behavior within quasi-periodic orbits in the phase space. The technique is appropiate to achieve efficient reduced order models even in complex cases for which the flow description requires adoi:10.1007/s00162-013-0293-2 fatcat:lpwcba7tjrccjasurolhg2q56e