  This paper introduces coordinate-independent methods for analysing multiscale
dynamical systems using numerical techniques based on the transfer operator and
its adjoint. In particular, we present a method for testing whether an
arbitrary dynamical system exhibits multiscale behaviour and for estimating the
time-scale separation. For systems with such behaviour, we establish techniques
for analysing the fast dynamics in isolation, extracting slow variables for the
system, and accurately simulating these slow variables at a large time step. We
illustrate our method with numerical examples and show how the reduced slow
dynamics faithfully represents statistical features of the full dynamics which
are not coordinate dependent.
