On the Space of Trajectories of a Generic Vector Field
Dynamical Systems
2015-03-17 v2 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1101.0778,
title = {On the Space of Trajectories of a Generic Vector Field},
author = {Dan Burghelea and Leonid Friedlander and Thomas Kappeler},
journal= {arXiv preprint arXiv:1101.0778},
year = {2015}
}
Comments
65 pages, 19 figures