  Finite-time coherent sets represent minimally mixing objects in general
nonlinear dynamics, and are spatially mobile features that are the most
predictable in the medium term. When the dynamical system is subjected to small
parameter change, one can ask about the rate of change of (i) the location and
shape of the coherent sets, and (ii) the mixing properties (how much more or
less mixing), with respect to the parameter. We answer these questions by
developing linear response theory for the eigenfunctions of the dynamic Laplace
operator, from which one readily obtains the linear response of the
corresponding coherent sets. We construct efficient numerical methods based on
a recent finite-element approach and provide numerical examples.
