  Multivector fields and combinatorial dynamical systems have recently become a
subject of interest due to their potential for use in computational methods. In
this paper, we develop a method to track an isolated invariant set -- a salient
feature of a combinatorial dynamical system -- across a sequence of multivector
fields. This goal is attained by placing the classical notion of the
"continuation" of an isolated invariant set in the combinatorial setting. In
particular, we give a "Tracking Protocol" that, when given a seed isolated
invariant set, finds a canonical continuation of the seed across a sequence of
multivector fields. In cases where it is not possible to continue, we show how
to use zigzag persistence to track homological features associated with the
isolated invariant sets. This construction permits viewing continuation as a
special case of persistence.
