  For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten
chain complex can be defined. The associated Morse homology is isomorphic to
the singular homology of the manifold and yields the classical Morse relations
for Morse functions. A similar approach can be used to define homological
invariants for isolated invariant sets of flows on a smooth manifold, which
gives an analogue of the Conley index and the Morse-Conley relations. The
approach will be referred to as Morse-Conley-Floer homology.

Dynamical Systems;Differential Geometry