  Dynamical systems are often subject to forcing or changes in their governing
parameters and it is of interest to study how this affects their statistical
properties. A prominent real-life example of this class of problems is the
investigation of climate response to perturbations. In this respect, it is
crucial to determine what the linear response of a system is to small
perturbations as a quantification of sensitivity. Alongside previous work, here
we use the transfer operator formalism to study the response and sensitivity of
a dynamical system undergoing perturbations. By projecting the transfer
operator onto a suitable finite dimensional vector space, one is able to obtain
matrix representations which determine finite Markov processes. Further, using
perturbation theory for Markov matrices, it is possible to determine the linear
and nonlinear response of the system given a prescribed forcing. Here, we
suggest a methodology which puts the scope on the evolution law of densities
(the Liouville/Fokker-Planck equation), allowing to effectively calculate the
sensitivity and response of two representative dynamical systems.
