Linear flows and Morse graphs: Topological consequences in low dimensions

The main aim of this paper is to show some specific connections between linear dynamic and graphs. Precisely, the Morse decomposition of a linear flow on the Grassmannians induces a directed graph. We apply the results appearing in Ayala et al. (2006, 2005) [2,3] and Colonius et al. (2002) [4] and compute the associated graphs for linear flows in dimensions two and three.