A trajectory-free framework for analysing multiscale systems
  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. 
Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl
math.DS