  In this paper we introduce filtration pairs for isolated invariant sets of
continuous maps. We prove the existence of filtration pairs and show that, up
to shift equivalence, the induced map on the corresponding pointed space is an
invariant of the isolated invariant set. Moreover, the maps defining the shift
equivalence can be chosen canonically. Lastly, we define partially ordered
Morse decompositions and prove the existence of Morse set filtrations for such
decompositions.
