  This paper describes the construction of a canonical compactification of the
space of trajectories and of the unstable/stable sets of a generic gradient
like vector field on a closed manifold as well as a canonical structure of a
smooth manifold with corners of these spaces. As an application we discuss the
geometric complex associated with a gradient like vector field and show how
differential forms can be integrated on its unstable/stable sets. Integration
leads to a morphism between the de Rham complex and the geometric complex.
