When a topological space is known only from sampling,
persistence provides a useful tool to study its homological
properties. In many applications one can sample not only the space,
but also a map acting on the space. The understanding of the
topological features of the map is often of interest, in particular
in the analysis of time series dynamics but also in the dynamics
of a map or differential equation given explicitely when the rigorous study
is computationally too expensive and only numerical experiments are available.