On the Space of Trajectories of a Generic Vector Field

Details On the Space of Trajectories of a Generic Vector Field On the Space of Trajectories of a Generic Vector Field

2011-01-04

arxiv.org/abs/1101.0778v2

Mathematics

Dynamical Systems

65 pages, 19 figures

Scientific paper

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.

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