2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67041We find conditions which guarantee that a given flow on a closed smooth manifold admits a smooth Lyapunov one-form lying in a prescribed de Rham cohomology class. These conditions are formulated in terms of Schwartzman's asymptotic cycles of the flow.11 pages, 1 figureDynamical SystemsAlgebraic Topology37B25, 37C99text