2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70074We give necessary and sufficient conditions for the existence of smooth Lyapunov 1-forms for the flow of a smooth vector field in terms of the behavior of certain locally finite invariant measures. The main statement generalizes a result of Schwartzman, whereas the methods are adapted from work of Sullivan.20 pagesGeometric TopologyDynamical Systems57R25; 37B35; 37B30text