  Understanding the macroscopic behavior of dynamical systems is an important
tool to unravel transport mechanisms in complex flows. A decomposition of the
state space into coherent sets is a popular way to reveal this essential
macroscopic evolution. To compute coherent sets from an aperiodic
time-dependent dynamical system we consider the relevant transfer operators and
their infinitesimal generators on an augmented space-time manifold. This
space-time generator approach avoids trajectory integration, and creates a
convenient linearization of the aperiodic evolution. This linearization can be
further exploited to create a simple and effective spectral optimization
methodology for diminishing or enhancing coherence. We obtain explicit
solutions for these optimization problems using Lagrange multipliers and
illustrate this technique by increasing and decreasing mixing of spatial
regions through small velocity field perturbations.

Dynamical Systems