We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3) distill the reduced slow dynamics on a suitably designed subspace. By avoiding trajectory integration, the developed techniques are highly computationally efficient. We corroborate our findings with numerical simulations of a test problem.
@article{arxiv.1412.7268,
title = {A trajectory-free framework for analysing multiscale systems},
author = {Gary Froyland and Georg A. Gottwald and Andy Hammerlindl},
journal= {arXiv preprint arXiv:1412.7268},
year = {2014}
}